I've finally seen a direct head-to-head comparison between the D600 and the 6D, and it's not as cut-and-dry as some people seem to think it is. In three areas that are very important to me, the 6D actually wins:
1. ISO range. The 6D has two full stops more high ISO settings at the top of the range. Based on my experience with Canon cameras, I expect this difference to show up in real world performance. This is an extremely important feature to me.
2. AF sensitivity. Yes, the 6D has a very disappointing 11 point AF system. It's irritating that Canon clings to these basic AF units. On the other hand, the AF is one stop more sensitive in low light than the state-of-the-art unit in the 1Dx and 5D Mk III, and two stops more sensitive than the AF in the D600. I love to shoot in ridiculously low levels of light, and coupled with the superior high ISO sensitivity, the 6D would seem to have the advantage in low light situations.
For my style of shooting, this is much more important than dynamic range, and Nikon's sensors lose that advantage at high ISO's.
3. Weight. I've been dying for a smaller, lighter FF camera from Canon. The 6D is a full 80 grams lighter than the D600 with the battery installed. This sounds like an awesome walk-around and backup camera. I intend to buy one to back up my 5D Mk III, as its specs are superior to the Mk II's in ways that are very important to me.