As you can see there is no major difference between these two camera, both shares same core specification and body design.
After a quick research and reading detailed specification + press release of both the camera we found that…
1. Oil issue solved
2. New “Quiet continuous” mode is introduced – After activating the silent continuous shooting mode you can capture 3 fps with limited mechanical noise.
3. Improved white balance with D610
Verdict: New users should buy Nikon D610 camera but we never recommend D600 users to spend $2K and buy the same camera, D600 users should wait for D620 (OR D610 successor).