An AVR contains EVERYTHING in the same box, hence the inevitable close interaction between all the parts in it. Separates do just the opposite, separating all the parts so there is no negative interactions. The result should always be a purer, cleaner sound as long as carefully assembled with adequate cabling. It's expensive and time consuming to build but plenty worth it imo.
Moving to separates
Does anyone have an experience they'd like to share about going from just an AVR or integrated to using external amp(s)? My Integra AVR has 100 W per channel (class AB), all channels driven, and sounds very good, so it is not clear to me that there is any advantage to connecting its preouts to a separate amp. Might be a total waste of money. Please mention your specific equipment. Thanks!