I currently shoot with a 5D2, 5D3 & D800E.
First & foremost, at ISO 100 & 200 the image quality of the D800E blows the Canons out of the water - plain & simple. DR and detail are stunning. If you shoot a lot at these low ISOs you can't get better than the D800E's sensor. At those low ISOs, in a high DR scene, a shot that only needs one exposure with the D800 might very well need 2 with the Canon to capture clean shadows. At ISOs 400-800 the DR and IQ are generally about equal with the exception of more details for the D800E. At above ISO 800 the 5D3 starts to pull ahead in DR and maybe noise but I find the noise of the D800E files easier to deal with.
As for AF, I agree with others that the 5D3 has an edge.
As for ergonomics/shooting comfort overall I prefer Canon but not by much. The one design feature the D800E has that's inexplicably missing in the 5D series is a built-in viewfinder curtain. What is Canon thinking? And why neither cam has a flip out, tilting LCD screen is a real mystery.
Oh, and Canons liveview is way, way better than Nikon's.
As for build quality, the 5d3 is better. Same too for shutter noise/feel.
As for frame rate, I kinda like the D800 option of using a 1.2 crop to get 5-6 fps (resulting in a 24MP file) but it takes practice to mentally switch from a full frame POV to a smaller crop.
As for lenses, I've seen a lot of 24-105 vs 24-120 talk in the thread with folks saying the 24-105 is a lot better. I don't agree. I have & love them both for their usability and IQ and find them comparable. As for overall lens line-up, I prefer Canon for its amazing TSE lenses and L quality mid zooms like the 70-300 and 100-400 and 70-200 f/4 IS (but it looks like Nikon is about to announce its own 70-200 f/4 VR). On the wide end, Nikon has the wildly good 14-24 and useful 16-35 f/4 VR. I've rented a 14-24 to use on my 5D2 and wow, it's nice. I opted for a Zeiss 21 f/2.8 for the D800E but am still considering the 14-24 or 16-35 VR since I really like AF and handheld stuff.
As others have pointed out, your choice of body has everything to do with how you shoot and what you enjoy shooting. For ISO 100-200 use, the D800 smokes Canon for image quality and it's about equal up to ISO 800. The 5D3 might be a slightly better general use DSLR but not by much and only if you use higher ISOs and need a little better fullframe frame rate or slightly better low light AF.
If you can, rent one and find out for yourself how it'll work for your needs.
Oh, and BTW, my D800E does unfortunately have the left side AF problem (still need to send it in for repair). But on the other hand, my 5D3 exhibits wild light leak thru the viewfinder when I'm using liveview (really bad - not using the annoying/stupid external curtain isn't an option). Sigh, nothing's perfect.