you're talking projectors out of my range so take my thoughts with a grain of salt, but when looking between the jvc x35 and sony HW50, it seemed like the consensus was the sony was a little brighter, had less lag, and may have more reliable bulbs(jvc had issues last year). the result was the sony was better for gaming, 3D, watching sports.
on the flip side, the jvc was blacker, and had a better 2D picture for movies.
I have no idea if these issues scale up to the high end models or not. i'm sure the jvc still has a pretty bad input lag, but without gaming that's a non-issue really.
the 4k may be the biggest difference between the two. I don't know all the details on the sony, but the jvc is still really a 1080p projector with extra processing. it doesn't accept or support 4k resolutions.
based on your needs, i'd lean towards the jvc. but I do not really have any specific knowledge on the high end versions. just a general impression of the entire sony vs jvc lines.
Displays: Samsung PN64F8500/JVC X35
AVR: Pioneer VSX-1130K, 7.1/5.1.2 audio
Sources: HTPC(Enby), PS3, XBOX360, Wii
Control: Harmony One