It recently occured to me after Nikon announced that with a grip the D800 shoots 6 FPS that I can't find a single advantage to the 5D3 over the D800. Here's what I know so far:
5D3 vs D800/E by catagory:
Dynamic Range: Inferior
looks like it, by a lot
Color Fidelity: Inferior
this is not known yet, it's possible the 5D3 might be better, we will see
Noise: Equal
probably very close and thus effectively equal, but it's not 100% for sure yet
FPS: Equal (with a grip)
mixed
if you want fps for wildlife that is not really, really close in, then the D800 wins
if you can get close enough to frame as desired, then the 5D3 wins since it can do it at 22MP vs 16MP DX, so more detail and less noise
at much higher ISOs reach advantage of D800 goes away so the D800 has no advantages and then you have either similar noise and detail or less noise and more detail from 5D3 scenarios, plus without grip, so 5D3 wins
Video: Inferior
mixed, but probably much more of a 5D3 win
D800 has 1080p crop mode so it wins for distant wildlife
D800 has full signal out over HDMI so it wins for that (although many people will not be able to handle that, so it's a win only for the really serious)
but the 5D3 appears to have less aliasing and color moire and should have slightly better SNR and maybe less rolling shutter, pretty huge things, providing there is not lesser sharpness from the 5D3, the 5D3 wins and since this covers a lot of shooting, I think it more likely that it will turn out that the 5D3 gets the win for video and perhaps not by a little
Autofocus: Equal (both are pro level)/Inferior (no f/8.0)/Superior (better with fast lenses due to special f/2.8 sensors)
unknown at this point
White Balance: Inferior
possibly
Auto Exposure: Inferior
very probably so
In Camera Lens Correction: Inferior
no idea, maybe
Pop up Flash: Inferior
yes
Price: Inferior
unless you need 6fps
Resolution: Inferior
yes, noticeably
AA filter: Inferior
not fair to say, each has the filter it needs
I realize that the 5D3 has a better menu system, so that's one thing it can possibly do better.
yes, personally, I do not like the nikon UI
you can also add that the Nikons I think do flash metering better
and the D800 has intervalometer built-in