The D7100 will do a very good job for you. The D600 produces better images, period. You can't change the laws of physics, which you would have to do to obtain equal performance from the two cameras.
The D7100 is at the top end of the DX format. The D600 is at the entry level of the FX format. If you look at your own goals and needs and what you want to do in photography, I should think the choice between the two cameras would be pretty easy. I found that the top end of the DX format was not sufficient for what I wanted to do, and I bought a D600. I'm completely sure that it was the right move for me.