Depends what you are after, better high ISO, 2 stops more dynamic range, better colour depth, higher routine, sharper images, more cropping, RAW HDMI out, built in flash etc. This is the most popular move for people swapping from canon to Nikon, thousands of people went this route once the 5dmk3 and d800 were released and compared. If you want a modern body for landscape, architecture, still life, macro, studio and many types of wildlife then it is an obvious switch to make without any hesitation. For things like sports you have to think abit more about speed, but the 1.2x crop mode still nets you 24Mp images with a higher DR than the 5dMk3 and with a fast card will pull images at 5.5FPs, no grip required.
WRT to the D600 you have a modern high speed 39 point auto focus system inherited from the D7000 DX camera but further tuned. The downsize being the sensor points mostly cover the more central portion, which is actually an issue with all FF cameras since ere AF sensors cover th central portion. A little more pronounced in the D600 compared to D800 or 5Dmk3 but same kind of ball park. The sensor gives a couple of extra stop of dynamic range over the canons, better high ISO but not by much. However, if getting focus points right not the corners is important D600 likely wont please you, the d7100 however...
D7100 is really a dream camera for many types of photography (but no high FPS for the machine gunners). State of the art aps-c sensor that will give most FF sensors a run for its money. No AA filter gives sharp images with good glass. 54Pt professional grade AF system thtat cover a huge area of the frame. Also interting is a1.2xcrop mode, in which the focus points cover pretty much border to order across the frame.
But it is a crop sensor when it comes to depth of focus. For IQ it is not too far behind, very similar to the canon FF ( e.g. compared with 6d about 0.8 stop worse noise but 1.5 stop better DR).