So I just sent a 6D back for issues other than AF and ISO and get in a 5D3 and after a couple of hours with it all I can say is the 5D3 center point is a joke compared to 6D in low light. 5D3 won't focus at all on fabrics in moderately low light that 6D locks in well under a second. 5D3 is noticably noiser at hi ISO as well.
When you say "noticeably noisier", are you referring to raw files that haven't been subjected to noise reduction or in-camera-created jpegs? I'm currently renting a 5DIII to compare to my 5DII in low light (and otherwise), and I'm interested in the 6D too because of its low light abilities; so I'm interested in your reactions.
Coming to the 5DII from a Pentax K-5 I was greatly impressed by the Canon's faster and more accurate focusing (among other things), so I'm always amused to see people here complaining about the 5DII; but I do get the impression (and that's all it is; I've done nothing resembling scientific comparisons) that the lenses I've tried on the 5DIII focus more consistently precisely accurately than on the 5DII in any sort of light (not that I've had many complaints re the 5DII).