The D600 seems to have a slight size advantage, but how slight is "slight?"
Check out this shot of what appears to be the D7000 by itself. Look closer, though, and you will notice that the D600 hides quite nicely behind the similarly sized D7000. Apparently "slight" really is slight!
Do not get the two cameras confused, though. They may look simlar on the outside, but the full-frame sensor in the D600 will certainly raise the bar as far as photo quality goes.