The D7000 is a noticeable step up in pixel-level quality over D90, and probably a full stop better in high-ISO performance. For real-world output (reasonably sized prints or web) at lower ISOs, you probably don't notice much difference.
We have very little real-world examples from D600 yet, but if I can extrapolate from DxO's test, this puts D7000 at nearly identical performance to D800 in DX crop mode, and puts D600 very slightly below D800.
I'd extrapolate from that that D7000 is still King of DX, and D600 is probably slotting somewhere below it and above D90. Again, this is to some extent just an intellectual exercise since I doubt you'd be able to reliably call out which camera took what, looking at prints. Therefore I wouldn't recommend D600 as a DX camera to upgrade a D90.
As a move to FX while transitioning from DX lenses, if you've decided you see some advantage in FX then it's not at all unreasonable, although I'd probably transition the lenses first, since those hold their value better than camera bodies.