The Canon 5D Mark III and the Nikon D800 are the Cadillacs of DSLRs. If you're in the market for a top-of-the-line digital camera, there's a good chance it will come down to these two (although, certainly, there are plenty of other options).
Which should you buy?
Both cameras are exceptional; however, they're complete overkill for 99.5% of photographers.
Let's say you need a pickup truck because you'll be moving some items that won't fit in your sedan. You could buy a new F350 Super Duty starting at $35,000, or you could buy a new Nissan Frontier starting at $18,000. Both trucks will get the job done.
Most of you reading this don't need the Mark III or the D800. But you're probably going to buy one anyway.
If you already have a Canon kit, it makes sense to stick with Canon. And if you already have a Nikon kit, it makes sense to stick with Nikon. There is no reason to spend a whole bunch of money on new lenses and filters and such. Dance with the one that brought you.
But if you don't own either system, the Nikon D800 is the top choice, in my opinion. Really, you can't go wrong with either camera, but the D800 is just a little better than the Mark III.
Nikon raised the stakes by putting 36 megapixels on their full-frame sensor. Canon was seemingly unprepared and made only minor improvements between the Mark II and the Mark III. And, while 22 megapixels are more than enough, it pales when compared to the D800.
The Mark III does have higher ISOs available than the D800, and it might have lower noise at high ISO, too. But it is unlikely that you will ever use those high ISOs, so that is a minor win for Canon.
If you are a sports photographer, the Mark III shoots six frames-per-second while the D800 only shoots four frames per second. Another minor win for Canon.
If you plan to use the camera for video, the D800 has continuous autofocus while the Mark III does not. That could be very significant or completely unimportant to you.
The biggest advantage of the D800 over the Mark III is the MSRP. The D800 will cost you $3,000 while the Mark III will cost you $3,500. That $500 could buy you a lens. Or filters, tripod and a camera bag. Or it could pay for photography trip.
The Mark III will not attract photographers to the Canon brand, but it will appease those who are already Canon customers. On the other hand, the D800 will attract many photographers to the Nikon brand because 36 megapixels on a full-frame sensor for only $3,000 will be hard to pass up.