You're right....... both my ears AND brain told me it sounded better when I made the switch many years ago. LOL
It's a no-brainer(pardon the pun) when you compare an integrated receiver/amp that advertises let's say 100 watts over 5.1 or 7.1 channels and a dedicated amp that puts out let's say 200 wpc, all channels driven. The integrated's 100watts is typically being spread amongst all the channels and when it is driven at moderate to loud volumes, it's questionable whether it's even capable of putting out more than let's say 30 wpc.
The dedicated, quality amplifier is definitely gonna sound better and I'd be willing to bet that double blind tests would prove it.
Your ears and brain work together. Without your brain, I don't think your ears would have told you anything at all about sound quality! :-)
Of course an amp, as described, will have more power than an AVR as you described. But seriously, don't tell us that AVRs can only put out 30wpc?!!? Have you ever looked at measurements? Sure, the manufacturers inflate them and sometimes give one-channel driven, but magazines do measure this, and I can assure you I've yet to see one drop to 30wpc with all channels driven. I guess you were exaggerating to make a point?
But then the question is this: How much power are you really using? I think you'd be surprised at the results in most listening environments (it's probably just a few watts even at peaks).
And as for the blind tests, they have consistently shown exactly the opposite of what you suggest.