I recently got a D600. The big difference I see in the images is considerably more resolution and better high ISO noise performance. I also like the slightly larger body and deeper grip of the D600.
That said, I'm keeping my D7000. I love it for street photography with a small prime, and will also use it with my telephoto lens for extra reach, and as backup. It's a stellar camera, and I could be quite happy with just it alone.