Which one do you suggest?

These are full frame cameras and both are after the same dollars.
Therefore there is little difference.
Maybe individual preferences.

This goes back over 50 years.
People ask which is better Canon or Nikon.
The correct answer is YES!

You will be peased with either camera.

Here is another comparison site:

http://snapsort.com/compare/Canon-EOS-5D-Mark-III-vs-Nikon-D800

Go to a camera shop and get your hands on both cameras and pick the one that fells best in your hands.

..

...those cameras may be too sophisticated for your needs. High performance cameras rather beg for high performance lenses and good photographic skills and knowledge. If you are a beginner, most of the potential of the 5DIII and D800 may be lost. Put another way, a cheaper DSLR will take just as good (or bad) an image as more expensive cameras, because what happens before you press the shutter button is more important than what happens afterwards.