What makes one good amp sound better than another?

I currently own a pair of half-decent speakers, Martin Logan SL3, driven by a Adcom 5503 3-channel amp (one channel for my center speaker). This amplifier is rated 200WPC in 8 ohm, and 350WPC in 4 ohm, and has no problem driving the MLs. I have been told since the day I bought the MLs that these speakers will expose any deficiencies within my system my amplifier included, because its "transparent" sound. Now, I am thinking about potentially upgrade the amp to something more "hi-fi", maybe Classe or Bryston, or Parasound's new Halo amps. However, I still don't know how one amplifier can sound so much different or "better" than another, assuming both are solid state and relatively well-executed, with large power supplies and capacitors etc. For example, I used to think Krell is the pinnicle of amplifier designs, but then I read from various forums that Krell amps are good for bass but have rolled off highs. How is it possible (I mean rolled off highs?). If one lookes at their spec, I am sure the frequency response is not much different from other high-end amps. What determins the sound of a high-current, mid-to-high wattage amplifier? When people use words like "fast", "transparent" to describe an amplifier, what does that mean? How can one amplifier generate wider sound stage than another? Even if I have money for a $3000 or higher SS amp, am I really going to gain much more than my Adcom?
Run tube amps with your Logan's, you will hear a big difference. You will gain much much more!
I also have an Adcom 5503, which I used to drive three Magneplanar MG1.6 speakers. I changed to using CarverPro ZR1600 amps (digital, and rated at 600 wpc into 4 ohms) and I do believe that there was a significant improvement. But then, Maggies are known to respond well to high amp power.

The reason I was willing to try the ZR1600 was its very low cost (I paid $2520 for three of them) and favorable comment by others.

The Adcom is a perfectly respectable piece of equipment (although the brand is looked down upon by many audiophiles). No doubt it can be improved upon, but, how much, and at what cost? If money matters to you I would suggest that you demand a home trial with your speakers and associated equipment before laying down many kilobucks for a different amp. Only buy if YOU hear an improvement.
You are either a glutton for punishment or just got a new can opener, and wanted to see what kind of worms were in this can!

In spite of the fact that basic amplifier design has not really changed that much in the last fifty or sixty years, the differences are potentially extreme. Many of the changes have been designers adding their own tweeks to a fairly basic design.

At the risk of being overly simplistic, every connection is a loss of signal, and in my experience even things that are not in the signal path affect the signal path.

Lots of people were impressed when Nelson Pass went with a single gainstage with the newer X series amps. The sound benefitted from the shorter signal path.

I currently own my second Krell amp, but both of mine were from the FPB series. I can tell you without hesitation or qualification that there is no treble roll off with either of these amps.

As far as your question about spending money and getting a return for your investment, I will relate another experience. I had an Aragon 8008st amp. It was 200 wpc doubling down as the impedance was halving, down to 1 ohm. For no good reason I decided to sell the Aragon and replace it with a Krell FPB 200. On paper the two amps were virtually identical. There should have been no real difference. In my listening room the difference was night and day. Rather than going into all the details, you can see my review, if you'ew interested. http://forum.audiogon.com/cgi-bin/fr.pl?ramps&1043208372&openusid&zzNrchy&4&5#Nrchy
You stand to gain a lot, or you may gain nothing, but don't be fooled by specs and people who want to talk about the science of audio...

What was the question again???
Please consider system matching, room acoustics and personal prefernces. Not because you will drop some cash for a nice Krell amp (I have had them as well) will instantaniously bring substantial differences in your setup.

Yes, better power supplies help, mode of operation, component pedigree, etc.. but unfortunatly ther is not a rule-of-thumb for amplifiers updates just based on the money investment.

Hope this helps

Well, my reading on Krell amps is not that they have rolled off highes...it's that they have way to much high freq's and are hard on the ear!

Of course, I own a couple of Krell amps so know that the truth is that they are pretty neutral and will take on the characteristic of the source.

Many amps are not neutral and have been voiced to have a sonic flavor. Other amps are fine design but used in the wrong type of system/room/speaker configuration by their owners. Strain (weak power supply) usually makes or breaks an amp for me. Sonic flavor, I like mine from the pre-amp and source and in a very small dose.

Amps have as many differences between competitors as do any other components.

However, I believe there is one difference pertaining to amplifiers over other components:

When you find the right amp, it alone is by far the greatest contributor to a system's sonic pleasure. But finding the right amp can also be like finding a needle in a haystack.

A good way to try to draw distinction is to audition different amp models under the same brand using same front end gear and softward. e.g. for Musical Fidelity, try the A3.2, then the A308, then the kwp. Different price points, various circuitary, power, etc. You WILL hear the difference.
Better or different?
As stated from previos posts YOU MUST GIVE TUBE AMPS A TRY.
The Matin Logans will come to life with a ARC VT-60 if hooked up correctly or a ARC VT-100.Good Luck