I tend to agree with Perrone. DX mode is fine in terms of image size - equivalent to a D7000 - but framing the image in the viewfinder is a nuisance. The viewfinder is full sized with a line to indicate the DX crop. That means your viewfinder is less magnified than normal and much smaller - nearly half the size of the FX view.
I had a problem with my 24-70 lens last week and chose to use my D7000 backup rather than my 16-85 on the D800. I would only use a DX lens on an FX body in an emergency or special situation.
Now the D800 is a better camera than the D600. I have both and the D600 is small in the hand - like the D7000 - and has a less advanced AF system. The disadvantage of the D800 is potentially frame rate - if you shoot bursts at critical action. If you are timing the key action and have one image at the critical time, the D800 is fine. So frame rate is a matter of style.