What changes are audible in a power amplifier?
Sorry to disappoint, but not anything a user can alter, or even measure. It takes intimate knowledge of the circuit (and the design philosophy) to make these changes.
First, a high-current driver section that can rapidly charge and discharge the capacitance of the output section. These are often under-designed in both transistor and tube amps. The driver current affects slew rate, cleanness of Class AB transitions, and distortion above 1 kHz.
Secondly, avoiding current fluctuations in the power supply (caused by Class AB switching transitions in the output section) from affecting the input and driver sections (which are typically in Class A). Power supply variations affect the subjective quality of dynamic impact and clarity with dense program material.
Thirdly, in feedback amplifiers, adequate phase margin, preferably well in excess of "textbook" stability minimums. This prevents reactive speaker loads from degrading and stretching out the settling time of the amplifier. Settling time, by the way, is the time required to recover from a slew-transient overload. This affects the amp-speaker interface, and why some speakers don’t "get on" with some amplifiers.
All of these aspects are audible to the amplifier designer, and appear on internal measurements of the amplifier’s functions. They do NOT appear on external measurements of a "black box" under test. Unless you have designed amplifiers yourself, you, or a reviewer, are not likely to hear what changing these parameters sounds like. If you have, though, they are pretty obvious.
P.S. Reading between the lines, Class A operation and multiple independent power supplies makes for clean and stable amplifiers that have good subjective results. But ... true thermal Class A operation greatly restricts power output, and multiple independent power supplies also raise the price.
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.