The Canon EOS 5D Mark III is the world's best digital SLR. It easily lets us create smooth, clean, beautiful and colorful images in any sort of light. It handles much better my cheaper Nikon D800 and D800E; my 5D Mark III handles and sounds smoother, quieter, feels better and makes better-looking images than my Nikon D800E.
The 6D is a smaller, lighter version of the world's best DSLR, the 5D Mark III. If money or weight matters, the 6D is better; the pictures will be the same from each of them.
Perhaps this has been posted before, I don't know, since I tire quickly of the "let's roast the newly-released Canon DSLR and praise the newly-released Nikon DSLR" threads. But, I found it by looking for actual reviews of the 6D, and found it interesting, given KR's reputation.