Evolving from a avr to an av processor. Benefit?

Of course an upgrade to an av processor will be used for both ht and stereo.  An avp would join a b&w 803 d3, and b&w center htm2 d3 as fueled by a mc255 amp.  
So how much happier will this component family be if an avp joined the family (eg.  Arcam with dirac)? Seems an avp without Dirac these days could be problematic. Audyssey from marantz appears to be disappointing and troubling. 

I have two processors the Krell Showcase for movies and the Luxman CL38U SE for music. The difference between the two for music is night and day.

An AVR's amps are typically not very powerful (WPC specifications are usually for 1 or 2 channels driven, with a significant drop when multiple channels are driven), which means less dynamics and actual power to your speakers.

Technology is rapidly changing, so your AVR/preamp will become obsolete a lot faster than your amp.  Being able to keep a nice amp and upgrade just the processor section if there's some new feature you want/need is nice.  I think this is the 3rd processor I've used with my current 5 channel home theater amp.

To get the best of both worlds, consider an audio only preamp that has a home theater bypass option.  This setup can provide a much better two channel listening experience than using a home theater receiver or processor plus amp. 

Whether you have a receiver or separate amp home theater processor setup, there's a lot of crap packed into either one of those units, mostly cheap circuit boards and not much room for high quality parts.  Lots of compromise and a focus towards a kitchen sink of features, as opposed to a focus on sound quality.