Between the two of them, there isn't an overall "better" camera, but only a camera that more closely match your needs / wants.
Of course in detail they do trade blows where one is objectively better than the other. The D600's sensor is just better than the 5D III's in terms of dynamic range. But, just as a contrasting example, the 5D III has a better handling, and I'm ready to argue that its ergonomics / user interface is plain better as well, especially for fast-paced shootings (events, mariage, reportage, etc.).
Don't just read the spec sheets, try holding them in your hand for a while in a camera store if you can,
Consider their respective lens lineups,
And then weight their respective pros and cons depending on what you want,