Based off the posted specs, my comparison of 5D3 vs 6D vs D600
Resolution -- D600 wins with 24 MP versus 22 5D3 and 20 6D
Frame rate -- 5D3 6 per second, D600 5.5 and 6D 4.5
ISO capability -- Per posted samples on the net D600 is very competitive versus 5D3. 6D is an unknown.
Dynamic range -- Typically Nikon wins. I don't know that anyone knows for sure, but it is likely D600 wins this comparison.
Autofocus -- 5D3 61 points of world class AF, D600 39 points, and 6D 11 points.
Viewfinder -- 5D3 and D600 both 100%, 6D unknown but is likely less than 100%
Max shutter -- 5D3 1/8000, D600 1/4000, 6D unknown
Build -- 5D3 easily wins this, D600 still has partial magnesium alloy. 6D is noted as being "weather sealed" and APS-C sized, the construction is unknown
Micro focus adjust -- 5D3 has it, D600 has it, 6d unknown
5D3 is better than D600, but there isn't IMHO a huge difference per the above. For $1400 less the D600 is quite competitive. It is early but the D600 looks to be a substantial step up from the 6D. The frame rate is a bigger improvement from D600 to 6D than 5D3 to D600. Autofocus quality is a bigger improvement from D600 to 6D than 5D3 to D600 also.
Let me say I'm not trying to irritate anyone. The 5D3 is an outstanding camera. The 6D will be good as well, but... D600 appears to win the comparison easily versus it...
Dave