I know you were curious about the D600, I don't have one, I have a D800, but had the same lenses when I upgraded from DX to FX, so I'll give you my feedback based on my expirience, take what you wish from it. On FX I find that the sweet spot on the 70-300 VR seems to be f/5.6 from 70-150(ish) and then f/8 > 150mm. I enjoyed this lens on the DX due to the reach of 450mm on the long end, but overall on FX I also have to say this lens performs so much better than I expected. I was already expecting to toss the on the for sale forum and grabbing a 70-200 f/2.8. Maybe I will do that somewhere down the road, but I'm still holding onto this lens, it's a keeper, especially being so much more portable.
I tried my 16-85mm in DX on the D800. Compared to the D7000, I noticed a marginal difference, but that was more in color and dynamic range than any real sharpness increase. The best images were still @ f/5.6 from 16-50 and f/8 from 50-85mm, just like on the D7000. To be fair, that was about a total of 20 photo's that I took side by side with the D7000 and didn't even bother to save them in my library so I couldn't go back for a second look, so that is from memory.