I have A Classe amp rated at 100 watts per channel into 8omhs and 190 watts into 4omhs.I am looking at two speakers,one has an efficiency rating of 86 and the other 90.How important is this difference in the final sound quality?
oops that should be ohms.............my difficieny
I have A Classe amp rated at 100 watts per channel into 8omhs and 190 watts into 4omhs.I am looking at two speakers,one has an efficiency rating of 86 and the other 90.

Assuming both speakers are rated at 8 ohms, the 86 db rated speaker would put out 106 db at full 100 watt output on the amp. The 90 db speaker would put out 110 db with 100 watts. Note that 10db = twice as loud. so 110 db is twice as loud as 100 db. Also, the 106 and 110 db speaker output would be at 1 meter from the speakers.

How important is this difference in the final sound quality?

Not important at all to the sound quality. Power and efficiency specs have no more to do with sound quality then gas tank size and gas mileage ratings have to do with automobile quality.

Jmcgrogan2 is correct on how loud the peak sound pressure levels will be with each speaker. However, another thing to consider is how each speaker will sound (i.e. tonal balance), which will vary depending on not only the voltage sensitivity but the nature of the load. For this you need an impedance vs. frequency curve. For instance, many speakers have a combination of low impedance and a highly capacitive phase angle in the mid- to upper bass. If you use a tube amp you will probably run out of current in this region and the sound may become either lean in the bass and/or flabby and boomy in the bass. Since you are using a Classe solid-state amp you probably won't have this issue since SS amps usually have low output impendances, but still it is something to think about.
You should find out what the lowest and nominal impedance is for each of these speakers and that your amp is stable at this minimum impedance. Typically good quality amps are at least 2 Ohms stable. If your speaker dips below the amps impedance limit it will clip i.e overload the amp.

Speaker manufacturers usually suggest the power an amplifier should have to drive their speakers properly e.g 30-150 W @ 8 Ohms. Lets say both speakers have the same nominal impedance of 8 Ohms and minimum recommended power is 30W. This means that the 86db Speaker will need about 70W while the 90db speaker will only need 30W to produce the same volume.

Given your amp is limited to 100W the difference in efficiency can become significant as you would want your amp to run in effortless mode rather than strain as it gets closer to its limit.
Both speakers are 4ohm Thiels,I believe they go down to 2.3 ohm.
All being the same, I would go for the less efficient speaker. Bigger amps are normally not the quietest animals out there, and the more efficient the speaker the more likely you are to hear noise (if there is any).

Power-wise, it is unlikely that your amp will run out of steam with either speaker.

The Classe should be stout enough in the power suppply to be able to handle that 2.3 Ohm minimum. The good thing is that this a dip that is not present for most of the musical content. I am guessing one of these spekaers is the CS6. What I can tell you is that watts per channel do matter for these speakers. I had a Krell 300cx for a day before I traded it up to a 400cx and the additional WPC gave me more detail and soundstage with the CS6s. But I also had a large room to fill with vaulted celings. If your room is not too large this shouldn't be a problem for you.
How important is this difference in the final sound quality?

Not as important as how they sound to you. Get the one which sounds better.

The impedance of 2.3 Ohms is a wee bit on the low side....this would concern me as it makes these speakers in the "harder to drive" category. Remember that this speaker will take nearly FOUR times the current of an 8 ohm load and this will definitely restrict your headroom (the dynamics your amp can handle where the amp remains below clipping). A massive amp and the more efficient speaker may help in this case.
Both are Thiel speakers,the SC6 is,I believe rated at 86db and the new 3.7 at 90db.I have heard the 3.7s through three different amps,Krell and two different Classe,one of which was mine.The SC6 I heard through an Arcam 85 amp, in a barren unfinished basement.Of course the 3.7s did sound better in the perfect listening rooms,with more power,however the 3.7s cost more than double the amount of the SC6 and the SC6 is in mint condition.
Are you just thinking out loud Pegausxls?

No one here can make purchasing decisions for you. How much better, and how much you want to spend are personal choices that only you can make.
Is there any truth to the claim that, generally speaking, the same number of Class A watts play louder, or seemingly so, than Class A/B - I hear this all the time, but don't know if it is true.
Yes,Pubul57, there is truth in some watts sound better than other watts.No,Jmcgrogan2, I am not thinking out loud,there are many here that have already experienced what I am about to experience and some that can give good sound advice to help me in my decisions.
Efficiency is a relative rating. My speakers are officially rated at 90 dB. However, the manufacturer recommends a minimum of 100 watts, and "200 watts for full musical enjoyment". I've tried many different amps over the years and ended up with 400 WPC amps (at 8 ohms, my speakers are 4 ohms).

So, how can this be? I don't know how the 90 dB rating was identified (I suspect from the driver manufacturer, but who knows?) but they are less efficient than some speakers with lower ratings. It could be that more power is needed because of the impedance curve across the frequency band - they dip below 3 ohms at two points. Or it could be the complexity of the 1st order crossover. A friend who knows electronics looked at the crossover board and jested that all it needed was an input transformer and it could be it's own amplifier.

On paper you should get at least 105 dB from a 100 WPC amp driving a 86 dB speaker. Even allowing for headroom, that would be adequate for most of us in an average room. But all this relates to level before clipping, not "final sound quality". I don't think your question can be answered by anything other than a personal evaluation.
I have driven my Thiel 2.4 (87dB/M) to pretty loud levels with a 130W amp and you have a 190W amp. So there is really no issue with regards to not having enough power for either speaker except for the 2.3 Ohms impedence with the CS6.
Other things being equal--which they usually aren't--I'd certainly go for the more efficient speaker. The more efficient, the less power you need and the better potential to accurately reproduce dynamic contrasts. The less power you need, the less the voice coils will heat and the less the speakers will compress the sound. The less power you need, the more headroom your amp will have and--if you like to play loud music--the less likely you'll be to damage sensitive tweeters. Also, the more efficient your speakers, the freer you are to try a wider range of amplifiers. And so on.

In the interests of full disclosure, 35 years in the audio hobby has shown me that I more often enjoy efficient speakers. The four pair of speakers I have range from 92 to 100 dB.

It's also significant that one manufacturer's 86 dB may be almost the same as another's 90 dB. Most don't cite the parameters of the tests that established the efficiency rating they quote. The most important is whether the rating specified is for an anechoic chamber or for typical in-room conditions (the former is typically 3 dB less than the latter). The next most important is efficiency over what frequency bandwidth: the 86 dB speaker that maintains that efficiency over most of the audible spectrum may, overall, be as or even more efficient than the 90 dB speaker that was measured only at 1 kHz or over a relatively narrow bandwidth (say 200 Hz to 6 kHz).

Another issue is what sort of impedance curve is characteristic of a given speaker. An 86 dB speaker that never dips below, say 6.5 ohms impedance may be far less demanding on your amp than a 90 dB speaker that dips to 3 ohms.

As I said, "other things" are seldom equal, but when they are, the higher the sensitivity ("efficiency" is the term we commonly use, but actually refers to another parameter) the better.

Happy listening!