The "improvement in sound" that I am looking for in a "processor" over an AVR is the separation of channels and how the unit handles moving sound objects within the Atmos tracks. The reproduction of music at it's best would be a great feature of a processor also. My current AVR is an Onkyo TX-NR636 that has Atmos capability only due to a software upgrade. It has a pretty good Atmos/music playback, but I have to wonder how much better an Emotiva MC1 or the Tonewinner unit with power amps would be verses my AVR. Since there is literaly no one that has reviewed the MC1 yet has me wondering about it's true worthiness. Is the Emotiva MC1 a $1000 disappointment? I am hoping to buy one and the amps needed for my 5.1.2 system someday and see if separates are worth the money and hype. Now, all of the above is a great debate on gear, but that does leave out the audio mixing engineer's competance or the directors guidence or simply the low audio budget for the media. The best gear is just a fancy consumer of electricity without quality media to play on it.
If you have patience - wait for the Prepro flagship models from Onkyo...
However from my own past experience, the equivalent AVR models provide the same level of performance when used as a prepro - with the sole exception of lacking XLR balanced outputs.
In terms of clear seperation, and directional audio queues - the biggest difference I have heard in my system, has been the tuning with Dirac.
The thing that drew me to Dirac was having heard it at audio shows, in stereo setups - where the imaging, soundstage was clearly improved through its use.
Your speakers and room interaction have a far greater impact on perceived channel separation, than any of todays mid market and up level AVR circuits.... - which is to say, pretty much all the mid market AVR's and Prepro's will sound identical in terms of raw decoding - the differences will be in the amplification (speaker dependent, and if you are using the pre-outs, not relevant) - and in the Room EQ - and this last is the big one.
An Integra DRX 3.4 - can drive a 5.1.4 setup, has pre-outs, and is economical for a prepro with Dirac.