Dan Chung of DSLR Shooter News has done an excellent review of the new Nikon D800 in comparison to the Canon 5DMk3 from a videographer's point of view. I have borrowed the following text from Dan's review, please click through to read it all, it is a great piece of work.
The Nikon designers clearly had the 5D mkII in their sights as the camera to beat when designing the D800. I would go as far as to say they were largely successful and the D800 is better than the 5D mkII at most things. They could not of course know what the 5D mkIII was going to be like and in fact my 5D mkIII was the first one that the Nikon designers on our trip had a chance to play with.
Essentially the output from the D800 and 5D mkIII is very close. I would give it to Nikon for sharpness and the addition of the crop mode. The Canon has a clear win in terms of moire and low light performance. Personally I prefer the control layout and the colour rendition from the Canon (especially under mixed lighting) – others may prefer the Nikon.
As a multimedia camera for newspaper shooters who are going mainly to web in lower resolutions then frankly both Nikon D800 and Canon 5D mkIII are great and way better than any previous DSLR."