I think that a lot of people who report sonic improvements when switching to a higher-power amplifier credit the increased wattage, and nearly forget that they switched amplifiers.
I have an amp which allows me to adjust operating voltage between 24VDC and 48VDC....which corresponds to a range of 30 wpc to 120 wpc [into 8 ohms].
I have the ability to hit most any power output in between those numbers.
Thus, I have a pretty good idea of what kind of power is needed with this particular amp in order to get the best sound out of my speakers.
And that's because I can hear the difference.
When I run at low voltage, many of my speakers can sound thin-ish, unbalanced.
When I pump up the voltage to around 36VDC [65-70 wpc into 8 ohms] the overall tonal balance improves, the bass fills-in noticeably.
65-70 wpc suits most of my relatively inefficient speakers fine.
If I drop the voltage much below 32VDC [55 wpc], the sound generally starts to suffer.
I only own two sets of speakers which appreciate 100+ wpc....and they like it a lot.
I should mention that this amp will double-down into 4 ohms at any voltage with a sufficient psu.
Something I consider increasingly important as time goes on.