I don’t have equipment to quantitatively test the dynamics of autofocus systems. It has been my experience that the dynamics are what differentiate one phase detection AF system from another, for the most part. Properly adjusted — and, if necessary, tweaked for each lens and distance range — they all seem to focus about as accurately, providing they reliably focus at all.
So the tool that I have to evaluate the improvements in the D810 AF system is subjective comparison. I took two Sigma 50mm f/1.4 DG lenses, and mounted one on a D810 and one on a D4. In a room dim enough that the exposure meter read f/1.4 at 1/20 second at ISO 125, I set both cameras to AF51. I focused back and forth between a near and a medium-distance subject, alternating between the cameras. I also used different focusing points, keeping them the same between the two cameras. I used moderate and low-contrast targets. The D4 was a hair faster, but neither system hunted.
I turned down the lights so the exposure meter read f/1.4 at /10 second at ISO 2000. Same result.
I took the lens off the D4 and mounted it on a D800E. In the brighter light, the D800E was a little slower than the D810, In the dim light, the D800E could not reliably focus at all on some things.
I’d have to say that, for static subjects, the AF in the D810 is improved over the D800E, and nearly as good as the D4. If it has anywhere near the D4’s ability to track motion, it will be a big improvement.