Nothing's wrong with the D600, I just strongly prefer the D700. The biggest things it has going for it is it feels absolutely indestructible (and probably is, I've dropped mine from waist height onto pavement with only a slightly scratch on the lens casing for damage), handles better (meaning, buttons and such in better places and a large viewfinder) and the AF system is incredibly fast, faster and more accurate than the D600 by very noticeable amounts.
I've handled my friend's D600 and it just didn't click with me. It's a fine camera, but if I had to buy a full frame under two grand I'd still go for the D700 over the 600.
That said, I'm selling my D700 for the D800 because I want to make large, sharp prints and I need a video capable DSLR for a class in the fall, so uh, if anyone's interested in a full frame camera for relatively cheap, shoot me a message.