As in the famous words of Ron Burgandy, "Well that escalated quickly".
Let me clarify:
The 6D feels good in my hand, physically holding it. It is the perfect size and weight for a camera. The front grip is perfectly sized, and my hand wraps around quite nicely. The control layout is what does it in for me. I know many people like it, and for someone who doesnt need to change settings quickly this is perfectly fine. I like to move quickly, so I need something that feels like it can "take it". Something about the build quality, namely the buttons, make me feel like it is a bit fragile (even though I know it isnt any more fragile than similar segment cameras). I feel the same way holding the Sony A7 series, and many people LOVE them.
The D600/610 feels more robust, and while it doesn't feel quite as perfect a fit simply sitting in the hand, once you actually start using the body and having to slightly move fingers and your hand to adjust settings/etc, that is where it truely shines in my hand.
I just got back from Best Buy to do some test shots with a D610 and some of their lenses. Upon initial pickup, the 6D feels better/smoother, but once you start to use it the Nikon feels perfect. It's weird to try and convey, just how I feel holding each body.