"Watts" are a unit of power, not signal quality. What people mean by sounding better, or an amplifier having cleaner power is sometimes a matter of personal preference and how their ear reacts to the sound.
As strange as it might seem, Denon and Yamaha (just to name examples) have comparable lines of receivers/amplifiers with almost identical THD%, damping factors, frequency responses, and power supply construction - but there are distinct differences in what these models sound like when compared side-by-side. Some prefer the "warmth" of one receiver over the "harshness" of another, but someone else might describe the same pair as "muddy" and "sparkling". To each his own, you need to listen for yourself to see what sounds best.
I'd say you could universally agree that "clean" amplifiers are going to have a high signal to noise ratio, good channel seperation, low total harmonic distortion.
Greg