Using the AF-C and AF ON method is no solution for D800.

I am not having any problems with either AF-S or AF-C on my D800E. I tend to use AF-C and AF-On focus because I find it easier, but either way ends up about the same.

I know that without evidence that is pretty useless, so here is a test I just ran. I used my 85mm 1.8G to take pics of my kid (moving, not posing) at 1.8. Here are a series of 8 consecutive frames that I took over about a 1 minute period (i.e., no deletions, cherry picking etc.), cropped at 100% to show just where I was focusing. I completely defocused the lens in between each shot so as to be sure the PDAF system was having to do a fresh focus search.

The top row are all with AF-S and the bottom with AF-C. The crops are all from the identical spot on the frame, which shows you that I didn't nail the center of the eye in each shot. Ultimately, I'm not seeing much difference between the two sets and both are perfectly acceptable for my needs.