What contributes most to a change in how an amplifier sounds?

Everything for high end equipment. 
The best design & parts to meet some specs the cheapest way possible for mid fi equipment. 
 

An amplifier's "sound" is only apparent when connected to cables and a speaker. So it could depend on the capacitance of the speaker cable, or any steep phase angles the speaker has.

And, as mentioned, the power supply, which is why  the average receiver will not drive say, a Magnepan or some other type speaker  (hybrids, electrostatics and other exotic types) that places demands on the amp it usually can't handle.

A lower level of Dynamics, flatter line, is expected when impedance is lower?

@emergingsoul Dynamics comes from the signal not the amp. When it seems like the amp is more 'dynamic' the chances are extremely high that what you are hearing is actually just distortion masquerading as 'dynamics' due to how the distortion interacts with the human ear.

Class D operation sidesteps the annoying Class AB artifacts, but then you get deep into designing pulse-width modulators that are unconditionally stable, resist transient upsets, have good phase margin, and also have low distortion, even under dynamic conditions. Basically all the challenges of designing a state-of-the-art ADC and DAC that can also deliver power into complex and nonlinear loads.

@lynn_olson If you design a self-oscillating class D amp then you satisfy all these requirements. In a self oscillating amp you intentionally exceed the phase margin by adding so much feedback the amp goes into oscillation as soon as its powered up. The feedback loop is designed to only allow one solution for the oscillation, which is used as the switching frequency. This has the benefit of allowing much higher feedback without the problems caused by lessor amounts and having it poorly applied. It also solves the problem of noise caused when the switching frequency drifts. So this allows the amp to be dead silent even on horns.

@atmasphere ,

Thanks for making me feel stupid...

@atmasphere 

It all sounds amazing.  It's so complicated.  Very elegant prose.  SAT verbal score was kinda low so forgive me I don't understand this too well. Some scary things related to a D amplifier.  Wish I would've pursued an advanced degree maybe this would've helped.