1) If we are talking DAC quality, from mass market on up, most of the mid market and better AVR's/PrePros are mostly indistinguishable from each other in proper objective testing
2) Decoders are the same, they are licenced from Dolby or DTS... so doesn't matter which you go for
3) Mixer's can be different - the tracking between channels on surround can differ, and there are a few dedicated proprietary ones that can sound different - and in some cases excellent. Logic7 was the best on the market in its heyday - Logic16 today is available on Lexicon & JBL Synthesis gear, and should also be good - but Dolby Surround also does this function, and does a very good job... many people simply use DSU even if they own devices with other mixer options such as Logic16.... some debate on which sounds better, and on which sounds better under which circumstances. (some material may sound better with one, other material with the other!)
4) Room/Speaker EQ - there can be substantial difference in this area - but the quality of the result can be just as dependent on the room and the speakers involved... the mainstream (and now getting long in the tooth!) Audyssey software has improved over the last couple couple of years by providing more control through control Apps - where previously that was only possible on the more expensive processors with the "pro" option and the "pro" mic/tuning kit (which used to cost circa $1k alone). Dirac provides excellent results, and extends from mid market Onkyo AVR's up to the high end TOTL JBL Synthesis models.... Arcam, Lyngdorf, and Trinnov all have their own take on this, with some apparently spectacular results claimed for all of them.
This is where I believe most of the audible differences live. But Improvements / Gains over the un-EQ'd configuration differ substantially depending on how good the base installation is, what the flaws are that Room EQ tries to remedy, and how any particular RoomEQ system remedies those particular flaws.
So for any specific setup, you might be hard pressed to determine which of those would provide the best results, without spending massive amounts of time trying them all out back to back.
Today you can definitely get 99% of the performance of a $10k+ processor, in a $1k AVR - it is mostly software - and the software has become mainstream
How much is that last 1% of performance worth to you - will you get value (and is that last 1% real, or a mirage of confirmation bias?)? well that is always the "high end" question!! - and over the years, there have frequently been components in the midrange price brackets, that competed successfully with the high price "high end". They usually sacrifice bling - are understated - and overperform audibly.