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?
On what planet are different lenses, focal lengths, iso's, apertures, shutter speeds, white balance and tint values considered "same setting
I would suggest getting some camera calibration software, Adobe have a great free one, and a colour card to sort out your WB and tint issues.