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?