Based on the fact that it is meant for a crop sensor (DX format), there would be vignetting at wide angles, then less noticeable at 50mm. The extent of vignetting would have to be viewed personally, but it should be significant at 17mm.
Some people might tell you that the D90 would be sharper because it would use the center of the lens, which is the sharpest part. This is true, but misleading. First, the D600 is twice the resolution, which will capture a lot more detail and that translates into a sharper image. Second, to get the same composition on a crop sensor (D90) you have to back away farther from your subject. The increased distance also results in a loss of detail. At 100% resolution, the D600 may appear softer in the corners than the D90, but if you resize the 24MP images down to the 12MP of the D90 you'll see that isn't actually true. The D600 will be sharper in all circumstances.
Hi, Lee, I have not tried any DX lens yet. I believe it will be a little bit sharper since it's a FX sensor, despite the DX mode when you have a DX lens, you will be able to use it in FX mode even with a DX lens. As far as the vignetting, Nikon has the "Distortion Control" for many lenses, it should work for your Sigma lens as well, I guess, but not confirmed.
The D600 is a full frame body; therefore, if you used the 17-50 on the D600 as a DX frame, no problem. If you used it as a fullframe 24mp beast, then you would have to choose the vingetting function the camera on high, and probably shoot greater than f8.
A good lens would be the 28-75 tamron 2.8, as you can use this lens on a FF body at f2.8, and is not so expensive!
The Sigma 17-50 won't be much sharper on the D600. You can only use it in DX crop mode and will be 10mp. FX will vignette badly. I have the Tamron 17-50 and it's an amazing DX lens. I won't use it on the D600 though.