Is the d4 better at focusing than the d800?

I have two D800's sitting on the shelf, one is powered by the EN-EL15 battery and shoots RAW at 4 FPS max. The other is powered by an EN-EL18 battery it shoots RAW (DX) at 6 FPS. Surely you are not suggesting that one of those two bodies has a better AF system than the other.

Just because a faster FPS body needs to perform the AF function in a shorter time span than a slower FPS body, does not mean is does so nor does it mean that it does it well.

The D4 may very well have it's AF system tuned to a higher degree of accuracy/speed than the D800, I would be somewhat surprised if that were not true, but it will take some testing to prove it.