In analyzing this particular set of images from the Canon 5DIII and the Nikon D800, there are two conclusions that seem irrefutable:
1. At ISO100, the Nikon D800 has noticeably superior images out of the camera, due primarily to greater detail and dynamic range.
2. At ISO6400, the Canon 5DIII has noticeably superior images out of the camera, due primarily to significantly less noise.
That's what the speculation has been all along, and this one set of images bears this out. The 5DIII is the better low light tool, and the D800 is the detail/landscape/portrait king.
You can argue that noise reduction can be improved in post, whereas detail and dynamic range cannot, so maybe the D800 wins.
But it's funny, because when my jaw drops at an amazing image in the galleries on fredmiranda.com, I don't start drilling down to the pixel level to figure out why. I think, "Amazing light, great composition, outstanding quality." I don't think, "Oh, that must have been taken by Nikon or Canon" but instead, "Why is that photographer so much better than I am?"
For all the "switchers" out there (or pretend switchers), I can't fathom that you would dump your glass and familiarity with a UI to make a change from Canon to Nikon (or vice-versa), when both tools look to by quite exceptional. Also, if you are inclined, browse the forums of nikonrumors.com. It's funny to see how many of them are complaining that D800 75MB raw files are just too unwieldy for their workflow, and hoping Nikon will release a 20-24 megapixel option for them. For them, the grass is greener when there is low light. For you, the grass is greener when there is more detail.