Well, I shot Golf today, which unusually meant I was shooting the D4 and D800 together, about equally.
It's the D4 that's off. Quite far actually.
Bright, sunny daylight and it pretty consistently shot at 4500-4700 degrees (as read after the fact in Lightroom). The D800 was about 5000-5500, about where I expect and more to the point it looked right. Setting it with the dropper in lightroom kept it very similar to the D800.
About half way through today I switched the D4 from A1 to A2, without much if any effect (probably correct as it's aimed at warmer tones at lower temperatures).
The difference frame to frame (between the cameras) in similar scenes was huge, so I'm having to adjust all the D4 shots.
One of the few times I've really relied on auto white balance, as usually I'm on a particular field or place, not roaming a fairway. Kind of a pain. Going to have to see if I can use the fine tune to adjust (I've heard it is pretty finicky as you need larger adjustments at once end than the other, so not sure).