As said, small differences in power output will be completely inaudible. As will THD below 1%.
The thing which makes one power amp sound better than another is general circuit stability, especially under transients like cymbal strokes. Poor design can result in ringing or other artifacts, and that is what will result in horrible sound. Unfortunately specsheets don't tell you about that. Therefore if building an amp I'd look for a design that has had good listening reviews. More important than specs.
Sorry, I couldn't disagree with you more about listening reviews. For a start they're highly subjective by their nature and are influenced by other factors such as: brand, cost, aesthetics, speakers and room acoustics, where in the case of a decent Hi-Fi amplifier, the latter two to dominate to the extent the amplifier makes no difference to the sound quality. Even then, what sounds good to one person, may not sound good to another. Personally speaking, listening reviews, even positive ones, put me off, as they often smell of audiophoolery, even if none was intended.
It also depends on what the amplifier is for: Hi-Fi, guitar? Is the goal to produce pleasing distortion or audible transparency?
I agree, that not all specifications such as: imperceptible noise floor and THD, mean the amplifier will be audibly transparent and not misbehave, leaving undesirable artefacts under certain circumstances, but test and measurement is the way to eliminate these, not listening tests. Also don't get too hung up on these either, as what's measurable might not be audible and the reverse is never true: test equipment is better than anyone's hearing, despite what some people wish to believe.