In a covered arena, at night, there is no ambient light...the sodium lamps don't provide enough light to shoot w/o strobes, as at 1/640 @ f/7.1 even ISO 12800 doesn't allow enough light/exposure to make it anything but almost indiscernible.
The strobes provide all, or 90% of the light (I hate saying absolutes unless I am 100% certain).
Focus for the D600 was "back button" and I focused on the barrel, composed such that the barrel was at the right/bottom AF point. Thus, pre-focused, I wasn't worried about whether the AF system was fast enough. I used manual focus on the Canon 1Dx, since I don't know enough about Canon's to know how to enable back-button focus and remove that function from the shutter button...and it's not my camera (and the owner doesn't know, either. She just manually focuses).
So, both cameras were pre-focused on the barrel, shooting ISO 1250 @ f/7.1 or 6.3 (we dropped down a little when it got dark). Both shooting @ 200mm, both being shot from the same location relative to the barrels.
Thus, there were only these differences in the settings:
1Dx: 1/250, 70-200L f/2.8 IS USM lens (image stabilized) D600: 1/200, 80-200 f/2.8 AF-D lens (no image stabilization)
D600 is 24mp, 1Dx is about 22.3 mp
In looking at the photos, the ones with her camera were crystal clear, even zoomed all the way in. The D600 were very sharp until you zoomed all the way in, esp on the rider's face, where you could tell just a smidge of softness/ghosting (perhaps not the right term) when compared side-by-side. Given the colors of the horse and the flying dirt around their hooves, you really couldn't tell anything in that section of the images.
I'll know more as I shoot more today with both cameras.