I'm considering acquiring a new (for me) integrated, under $2k, to drive my KEF full range speakers. They are very efficient (93db) , 4ohm and rated for 50 - 200 watts.  It seems that a good amp with 80 or 100 watts per channel at 8 ohms will take these speakers to any volume I'd want to experience in my medium sized living room.  So what advantage/benefit in sound am I going to get with 150 -200 watts, or more, per channel? Is it worth spending more for extra power that will never really be demanded?  
I would say the benefit of more(quality) watts would be headroom.  Some specifics like how loud you listen and how large/small your room is should determine if you "need" more watts than 80/100 watts.

I have a Yamaha A-S1000 integrated amp with "only" 90w/ch and let me tell you it is the most potent 90w/ch I have ever heard/owned.  This thing is a beast at 48.5 pounds and it does not even break a sweat driving my Klipsch RB-75's(97dB) at ear bleeding levels in my 5000ft3 room.  I know the 75's are bookshelf speakers instead of full range but they do bottom out in the mid 40Hz region.

Going from 100 wpc to an amp with 150 to 200 wpc/8 ohms is not a significant increase in power. In terms of SPL, with 200w you would gain 3dB.

A high current amp with 80 or 100 wpc would be a better performer than simply going for higher wattage. High current amps will have better control over impedance demands from the speakers, in your case 4 ohm speakers.
I should add that since your speaker's impedance goes as low as 3 to 4 ohms, an amp that doubles it's power rating would provide you with high current. For example, an amp rated at 100 wpc/8 ohms, 200 wpc/4 ohms.
The plus side of your KEF's is the high sensitivity of 93dB, so I would say you don't need to look for a high wattage SS amp.
You could also try tubes, although the reviews I've read are using SS.
+1 Lowrider.  Look for a quality amp that doubles down in watts from 8 to 4 ohms. I run a BEL 1001 MK5. It is rated at 50 into 8ohms, 100 into 4, and 200 into 2. It will drive many speakers better than many 100 wpc amps will.  
I’m considering acquiring a new (for me) integrated, under $2k, to drive my KEF full range speakers. They are very efficient (93db) , 4ohm and rated for 50 - 200 watts. It seems that a good amp with 80 or 100 watts per channel at 8 ohms will take these speakers to any volume I’d want...

I agree with others regarding an amp that can produce high current and preferably double down in its 4ohm power output. Or at least come close.

You know the speakers are 4ohm rated, yet you say that an amp that is rated 50-200 wpc into 8 will get the job done??? Not necessarily if the amp does not have its 4ohm specs published. It could have a compromised power supply and not be able to generate the current needed to be stable at 4ohms. Just make sure the amp has a 4ohm rating too and because the KEF’s have high sensitivity, you’ll have no problems. There are lot of good ones out there in your price range.

My bad; these speakers are rated for maximum 300w at 4 ohms. So an amp with 150w at 8 ohms which doubles down to 300w at 4 ohms would be most I should use. Correct?
@larstosur In my experience you will get a little more 'control' of the music. By doubling the power does NOT equate doubling the max loudness. In general you will need 10X the power to double the loudness which is 3db. Our ears hear in a logarithmic curve not linear. But is that extra power worth it? You need to listen and make that decision yourself. From there there is many variables between different manufacturers. Most important would be 'current' reserves and how long can they be sustained especially for peaks. In most cases a few milliseconds is fine.
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My bad; these speakers are rated for maximum 300w at 4 ohms.

IMO, power handling ratings for speakers are among the most meaningless spec there is.  Impedance and Sensitivity are the specs that matter most.

At 93db sensitivity, a good 100 wpc amp into 4ohms will drive them to ear splitting levels in a medium sized room.  You do not need an amp that will produce 300wpc into 4 with these speakers. 

When you have extra power it fills out the sound with more authority with more powerful bass.Im using Pass 350.8  wonderful powerful sound getting more watts is always better.

When you have extra power it fills out the sound with more authority with more powerful bass.
True, ebm, but you're using a Pass amp with high power (watts), and also high current. An excellent design.
There are many amps which can produce a high amount of wattage and do not have quality power supplies. So, not all watts are created equally.

Larstusor, a 100wpc amp at 8 ohms that doubles into 4 ohms will be all the power you would need to drive your speakers.  In this case I would advise spending your amp budget on quality vs. quanity watts.

From looking at larstusor's previous threads, the speakers are KEF 105/3. The spec for sensitivity is 93db/1m/2.83v. Since this is a 4 ohm speaker, that 93db is using 2 watts. The sensitivity for 1 watt will be 90db, so not quite as high as it appears. Wattage can be very misleading. A 60 watt Pass class A amp will drive and control these speakers much better than a very cheap 200 watt amp. Considering your budget, you should be able to find a good quality amp of 100-150 watts @ 8 ohms that doubles or almost doubles into 4 ohms.

A few notes...

First, efficiency of 93 db is a moderate efficiency. Its likely though that these speakers are really rated by sensitivity instead of efficiency, if so then the actual efficiency if the speaker is 4 ohms will be 90 db. I just noticed the tis49 stated exactly the same thing above.

In the average size room 200 watts will be nice to avoid clipping when 'rocking out' but it will be right on the edge. I had speakers of 89 db 1 watt/1 meter and I found 200 watts to be barely enough power if I was pushing things.

Let's talk about 'current' for a moment- there seems to be the usual confusion about what that means on this thread (based on the use of the phrase 'high current') so let's go through the math:

Assuming 300 watts from the amp and a 4 ohm load, the power formula tells us that the current really isn't all that high:

Power = Current squared x load impedance

300 = Current squared x 4, solving for current we get 8.66 amps.

The thing to note here is that it makes no difference the technology of the amplifier, if it can make 300 watts into 4 ohms then the current will be 8.66 amps. If 8.66 amps does not seem like a lot to you, then we have the germ of a conversation you might want to have.

Its nice to use an amp with more than enough power to drive a given speaker past its limits. Of course you don’t want to push so far as to risk damaging your speakers. I like having more dynamic range on reserve for those bursts of sound that call for it. Not only with higher frequencies, bass sounds richer and fuller. The only time I pay attention to wattage rating and become intrigued enough to investigate more is when the amplifier is high current and watts double or close to double when impedance is split in half. Then I will check output capacitor and transformer size and VA rating of the power supply as a whole. Wattage ratings are not always very telling of an amplifiers performance. When I had a Sim Audio W 4070 that was rated at 70 x2 at 8 ohms it got me wondering why it sounded so much heftier than some other amps with double the wattage rating. Then it had me seeking answers. Looking at its specs and comparing them with other amplifiers. Search for meanings and get a feel what to look out for. The sim is a great "little" amplifier. Not many amplifiers will match its spec to size ratio. I would consider it above average in terms of power ratings and specs. 

P/S Transformer 750 VA
P/S Capacitance 100,000µF
Class Of Operation A/AB
Single Ended inputs (normal & phase-inverted) 2 pairs
Balanced inputs 1 pair
Input Device Type J-FET
Input Impedance 47,500 Ω
Input Sensitivity 750mV
Output Device Type Bipolars - 4 / ch.
Output Power @ 8 Ω 70 W/ch.
Output Power @ 4 Ω 140 W/ch.
Output Power - Bridged Mono 300 W
Bandwidth (+0/-3.0dB) 10Hz - 75kHz
Output Impedance 0.025 Ω
Damping Factor (static) 320
Gain 27dB
Signal-to-noise Ratio > 100dB
Maximum Output Voltage 26 V
Slew Rate 15V/µs
Maximum Peak Current 20 A
Crosstalk @ 1kHz -100dB
IMD unmeasurable
THD (20Hz - 20kHz) < 0.1 %
AC Power Requirements 120V/60Hz
Power, watts or amperage isn't going to tell how an amplifier will sound compared to another. I can only provide you my real life experience with Jeff Rowland products. I had a Jeff Rowland Continuum S2 Integrated Amp. The S2 is rated at 400 watts @ 8 ohms / 800 watts @ 4 ohms. I traded the S2 to purchase the 625 S2 amp. The 625 S2 is rated at 325 watts @ 8 ohms / 600 watts @ 4 ohms. Everything about the 625 S2 is better...the soundstage, bass, mids, highs, tonality. Unfortunately, specification don't always give an indication of how an amplifier is going to sound. The Continuum S2 is Class D and the 625 S2 is Class AB. My point is there are other factors that determine an amps sound that has absolutely nothing to do with its power rating. In my opinion, it's better to spend extra money to get a better sounding amplifier; not necessarily a more power amp!   
The again, not everyone hears the same...an upgrade to one could be nails on a chalk board for another!
True power specs shouldn’t be a be all when shopping for an amplifier of course. But always very helpful indicators because no one likes leaving half of a steak sitting on a table. The drop in power could just mean the lesser still had adequate power to bring out the speakers strengths according to your likes. Its obvious you like the new amp for other said reasons. Be that as it may. If it lacked enough power to push the attributes in the new amplifier and bring forth the qualities you like in the speakers your using I doubt you would be as fond of it. Ive seen people blame speakers, or even feel content with speakers. Then switch to an amplifier with more current even close in design then see the speakers they thought they knew so well in a much brighter light.
I run 125 wpc on some 93 db B&W 803's and have to use another amp to drive subs. If you are going to have tone controls and plan to use a bit of bass boost, more power might help. otherwise, the actual difference between 80 and 125 watts is pretty moot, maybe a db in sound level. One db is defined as the actual threshold of change in volume we can hear.

Usually, I do not use my subs and probably wouldn't even need them in a normal house that is divided up more. My house is one relatively big room with two bedrooms on the side away from my speakers.

More important than the actual watts is how these watts work, i.e., how big is the power supply. If the power rating on the amp is at 1000 cps, for example, the power supply is probably too small. If the rating is full range, at least 20-20000 cps, it is what you want. 

I also have an Adcom 65 wpc amp that is heavy for what it is, meaning a big transformer.   For a $50 Craigslist amp, it did quite well pushing two pairs of very inefficient B&W DM 14/1400's, and it was loud enough; however, since these speakers mute the sound when an amp clips, the speakers did shut down much sooner than with the amp with twice the power, meaning it could have blown tweeters from clipping the signal, because of too little power. 
Watts is like HP - it tells you nothing about the torque, it will give you a hint how fast (loud) a car can go but thats useless when you listen in the 1 to 5 Watt range at 80 to 90 db. Its about the instant acceleration, how much torque and at what rpm it will be available. Some speakers (heavy cones) need a high damping factor for the bass but the mids and highs will suffer because the most immediate and best sounding amps are pure high current CLASS A with low feedback.
Krell Vanguard
I’m considering acquiring a new (for me) integrated, under $2k, to drive my KEF full range speakers. They are very efficient (93db) , 4ohm and rated for 50 - 200 watts. It seems that a good amp with 80 or 100 watts per channel at 8 ohms will take these speakers to any volume I’d want to experience in my medium sized living room. So what advantage/benefit in sound am I going to get with 150 -200 watts, or more, per channel? Is it worth spending more for extra power that will never really be demanded?

There are several such discussions on Audiogon if you care to search the archives. Use key words like "spl distance" or "watts needed" or "watts required".
One such discussion is here:

like I wrote on the above cited thread, there is a drop off in SPL at your listening chair vs. the actual spec of the speaker.
Your speaker is mediocre efficiency (I agree with Atma-sphere on this).
Do you listen at 1m away from the speaker? Most likely not.
You are most likely seated 3m (~10’) away.
You, in particular, get further dinged because you informed us that your speaker is 4 Ohms & 93dB SPL. Since the industry spec for listing sensitivity is 1W into 8 Ohms & your speaker is 4 Ohms, you would be feeding 2W into your speaker. So, if we normalize your speaker sensitivity to 8 Ohms, it is actually 90dB (I think another member already pointed this out to you).
OR, if this is confusing to you - IOW, I would have to reduce the input power from 2W into 4 Ohms to 1W into 4 Ohms (per industry standards) & then your speaker will measure 90dB/1W into 4 Ohms/1m.

For every doubling of distance the SPL drops by 6dB. So 1m --> 2m, the SPL = 90 - 6 = 84dB.
Then, 2m --> 3m you lose 3dB (didn’t quite double the distance but increased it by 50% only). So, now the SPL at 3m = 81dB.
Add 3dB for stereo listening.
Subtract about 3dB due to damping effects of rugs, furniture, curtains, walls, house plants, etc.
This addition-subtraction is a wash-out so we are still at 81dB SPL at 1W at 3m listening position.
10W: SPL = 91dB
100W: SPL = 101dB
200W: SPL = 104dB
400W: SPL = 107dB

You can see from the calculation above that if you used a high current 100W amp you could achieve a max SPL of 101dB at you listening position. Reasonably recorded rock, definitely well recorded Jazz & Blues can exceed this SPL number & for sure well recorded classical music.
Realistically you want an amp to reproduce atleast 110dB SPL for your (sudden) peaks in your music program to give you the feel of easy-of-delivery, realistic & dynamic playback, etc. For your particular speaker, you can see, you will need some serious watts. Not only watts but you will need high current watts since your speaker is 4 Ohms (& most likely has some very crazy phase angles meaning that the amplifier will be dumping current into an impedance that is most likely lower than 4 Ohms). This will get expensive for you, no doubt. And, this is also what Ralph/Atma-sphere alluded to in his post date 04-25-2016.
So, the answer to your question is: yes! it is worth spending extra $ on a 200W/ch high-current amp....
(I believe that you can never have enough watts for playback! ;-) It's a mistaken notion that those (supposedly) extra watts are not needed....)