I'd go 5d3 over 6d if your only snagging 1 FF body. I am currently using both the 5d3 and the 6d for wedding work and the files from both look pretty damn close (its odd, I do find some situations where I like the colors for the 6d better, then vice versa).
For weddings though, reliability is a huge factor to consider. And on that level, the 5d3 wins hands down. I would not buy a 6d as my main body, though I do truly like the camera, there are some shortcomings to it that are hard to move past.
Here are 2 images - both unedited, one from the 6d and one from the 5d3, same setting, can any of tell which one is from which camera?