I am also seriously contemplating the D600. I use a D7000 now. I will always have a crop sensor Nikon, for as long as they make them, since I shoot sports, and can't afford really long telephoto lenses. My 70-300 VR has an effective FL of 450mm on DX. To get that with FX, I'd either need the 80-400 VR focusing dog, or a $9,000 lens. Also, my D7000 shoots at 6 FPS, which is marginally (OK, probably meaninglessly) faster than the D600.
That said, except for the smaller file size of D7000 images (compared to D600 images), I can't think of another reason to own the D7000 over the D600 other than price (camera and DX lenses). If I didn't shoot sports, I'd never need a lens longer than 300mm on FX. Now that the D600 is the same size and weight as the D7000, the compactness advantage of DX is gone also.
I do agree though with those who posted above - don't buy a D600 and put DX lenses on it. That is a waste of money if you already have a D7000. I doubt you'll see any appreciable gain in image quality. Buy a couple FX lenses first or at the same time - even if they are small inexpensive primes (a used 20mm AFD is AWESOME on FX, for instance, and the 50mm f1.8 is also great to have and very cheap). If you've never shot a film SLR or FX digital, you will truly be amazed at what an f1.8 lens viewfinder looks like on FX. It will blow you away.
Throughout the history of photography, the larger the imaging media (plate, film, sensor) the better the image. 35mm was better than APS, medium format was better than 35mm, large format was better than medium format. FX is better than DX. With no size/weight advantage, and if I could afford to pay twice as much for the camera, there is no way I would ever choose DX over FX unless I needed the crop factor.
That said, if all I did was make snapshots, and I never enlarged a print bigger than 8x10, all I would ever need is my old D50, because with that subject and print size, the product difference is negligible. So it depends a great deal on what you want to shoot.