If the 6D is supposed to focus better in low light, why has the 6D failed to initiate focus in situations I mentioned, where the 5D3 hasn't had the same issue? ...
I could not answer that, it is the opposite of the experiences I had.
Anyway, I still believe the 5D3 is by far the better "all around" camera for a lot of reasons.
But that the 6D offers slightly better IQ, slightly better noise handling, and slightly better AF in "some situations" , and has some features that some people want that the 5D3 does not have (wifi etc.) for about $1K lower price, well, that's a pretty good deal!