My personal bent on this, after having designed, modified, and lived with numerous amplifiers over the years with differing topologies and active components, is that the question is really too complex to answer. There are too many different parameters of an amplifier that can and do change the sound. Our biggest problem is the specifications that people typically look at when trying to compare amplifiers. They are mainly meaningless, other than to quantify a measurement that is performed on a test bench with a contrived load that does not in any way resemble a loudspeaker. The interaction between amplifier and load is extremely complex, and the math involved is even more daunting because with music you are dealing with a constantly moving target.
A good example that I can thrown out there is if we were to take a fictional Class A/B amplifier and Class D amplifier, both with identical power supply capability and both rated at 100 watts into an 8 ohm load, at 1kHz with 1% THD. They both have a frequency response at 1 watt of 10Hz-30kHz. These two competently designed amplifiers should sound similar if not identical if run within their rated power. Listening to them they sound totally different beyond a certain listening level. Why would that be? Well, we have not speicified the power bandwidth of the amplifiers. Turns out the Class A/B example can deliver full power at all frequencies, but the Class D example has limited output power in the low bass and high treble. There are numerous cases, such as the one described, that CAN account for two similar amplifiers sounding different. Throw a transformer-coupled tube amplifier into the mix and now you have added non-linear frequency response to the table!
