OK, what is the difference between BMPC 4K Pro Res or CinemaDNG RAW? Which has higher resolution? Which offers more latitude than the other in color correction? What's the benefit of one over the other?

CinemaDNG is a version of Adobe's Digital NeGative format extended for motion picture capture. Like other raw formats, it's nothing but raw sensor data.

ProRes is a compressed format that's very suitable for editing. The compression it uses is selectable, and in the HQ setting it's very light. It's already de-Bayered, which means that it contains color information and in most cameras it's chroma subsampled to 4:2:2. In some higher end cameras you can record 4:4:4:4 which is basically straight from de-Bayering into the codec, and uses light compression so its quality is quite high, but nowhere near as big as raw.

CinemaDNG is 12bit whereas ProResHQ is 10bit.
Some people shoot everything in cDNG and others find ProResHQ is great for all but the most demanding post workflows. ProResHQ so blows away 8bit AVCHD/H.264 as far as being able to push grading that I fall into the latter camp and use ProResHQ.

I only have the 2.5k version, but another way to look at it that the difference between DNG and ProRez/DNxHD is getting 5 hours of video in a 480GB SSD instead of an hour or so. That's how I net it out since the classical orchestra concerts I video run close to 2 hours and are going to wind up on YouTube or the equivalent.

The economics of 5 to 1 are pretty compelling UNLESS there's some specific reason why I need the higher resolution. Which there sometimes is.

ProRes/DNxHD are pretty damned good and mostly good enough. And did I mention the 5 to 1 $ advantage? If SSD's get up to a couple of TB and down to a couple of $ hundred I might change my mind.