Welcome!

What do you like to / plan to shoot? The bottom line is that both are excellent cameras. I'd say that the D800 is more studio/landscape oriented (high res, slower), whereas the 5DIII is more wedding/event/general purpose oriented.

Your comment about lenses is a valid one. Assuming this is your first dSLR purchase, you're not buying a camera, you're buying into a system - bodies, lenses, flashes, etc., and the body is the one most likely to be replaced down the line. Three years ago, I made the Canon vs. Nikon choice at the entry level, and actually part of the reason was the excellent reviews of Canon gear here on TDP (nothing similar for Nikon, really, at least until Bryan does full text reviews for their lenses), and another part of the reason was the posts here (TDP forum was then, and remains to a large extent, Canon-oriented). At this point, changing would be very difficult for me, not to mention expensive.

The ergonomics of the two are pretty different - try to find a shop with both so you can hold each of them.

As for lenses, both Canon and Nikon have a lot of overlap, but some distinctions - and that's where what you like to shoot really matters. Nikon has nothing to match Canon's TS-E 17mm, MP-E 65mm, or 8-15mm Fisheye, 28-300L, and the Canon 24-105 is better than the Nikon 24-120 counterpart. Canon has nothing to match the 14-24mm f/2.8 or the 200-400mm VR (at least as a real, purchasable lens, not a 'we announced development of one but we haven't announced it for real and even if we do it'll likely be well over a year before you can buy one' lens).