If the goal of an audio component is to reproduce the music as faithfully as possible, any coloration that is introduced is undesirable from such a perspective. Based on their shortcomings, amps will introduce artefacts in the form of noise, distortion, clipping etc that are essentially their sound signatures. Where do these shortcomings reveal themselves in an amp?
Current output, power bandwidth, THD, quality of: capacitors, transformers, power supply, circuit design, isolation, clipping performance -- all these and more impact an amps performance. To say that all amps at the same power rating have more or less the same sound signature..I don't know what to say.
Actually, most of the times, the distinction in sound signature (read that as distortion) is introduced by the manufacturer intentionally to distinguish their products from others. Amps are qualified as warm, rich, bright etc etc etc, all these are distortions, only neutral (aka transparent) is ok. If your amp is warm or bright, its a bad amp which is designed to work with bad speakers. If the sound on my cd is not warm, why would an amp that produces warm sounds be called good? How many times I've heard, I have bright speakers, I need warm amp (or worse, warm cables), why cant people just buy neutral speakers and amp, instead of buying warm speakers and bright amp.
Its not all that hard to make a neutral amp, you actually have to make an effort to make that same amp sound warm or bright.