Upper and Lower Box opinions
I've only paddled the Upper Box three times (1000,1100, and 1350 cfs) and the lower box once (1500-ish cfs). But here's my thoughts.
I feel that the Upper Box would be kinda pushy above 1500 cfs. Most of the rapids are like Kirschbaum in Gore with a few Pyrite, Scissors type drops thrown in the middle/top/bottom of them or Barrel Springs-ish. At 1350 cfs, we could read and run a good bit of it, but got out to scout five or so times. We walked NCO falls and Big Arsenic. If I was a little more familiar/comfortable with the run, both drops might go. The run to the Little Arsenic trail took us two and a half hours or so. At the current flow, be prepared for "game-on" style paddling. Lots of big waves, fast current, sticky holes, true scrambling class V paddling (and a nice sweaty 50 minute hike out after Little Arsenic if you don't want to paddle the 7 miles of flatwater to Dunn Bridge, but it's a short shuttle). If you've not run it before, prepare for a long day. I would put it a notch above Gore Canyon in difficulty at similar flows. But, maybe that's because I know Gore better than the Upper Box.
The Lower Box is considerably easier. Mostly moving flatwater with some down the middle class II-III and three or four class IV-ish rapids towards the end. Easily scoutable, no consequenses below most of them. The one rapid on the Lower Box that is close to the rapids on the Upper is Rock Garden (just throw some pourovers and ledges into the middle of it).
I think that the Pilar section would have some great on-the-fly playboating at it's current level, but would be a quick roadside run (four miles or so).
It seems with all the warm weather, the river levels are going richter down there right now and rising quick. I wouldn't venture into the Upper Box unless you are comfortable with Gore Canyon above 2000cfs. I don't imagine there's a level that's too high for the Lower Box or Pilar. All of the creeks except maybe the Red River are pretty stompin, right now as well.