Yes exactly! I like both Canon and Nikon,if D810 feels in hand also so comfortablelike 5D Mark III I'll buy a D810,if not - 5D Mark III.
D810 is much better than 5D Mark III I think in every way: AF,Megapixels,Lens seems like have more resolution than Canon Lens (I think thats why Canon doesn't have a high Meg.Camera),buts its just my IMHO.
I really like 5D Mark III,just need to compare it how both feels in hand.
Also read Ken Rockwell about auto-focus on Canon camera (in this case 5D Mark II,I think 5D Mark III have the same) : "Unlike the 51 AF sensors with real facial recognition in Nikons, the all-sensor position of the 5D Mark II isn't very smart. It won't focus automatically on eyeballs, it tends to focus on whatever's closest. "
Thats why I also more toward to Nikon,seems like AF is extremely accurate.
I think you'll enjoy the 5D III ergonomics better. The hand well on the 5D III is nice and deep, and so you feel like you have a very solid grip of the camera. That comes in more useful with heavier lenses. It comes in extremely useful, actually. You'll love it.