If you place an FX lens on a D7000, you will not get the same Image Quality as using the same lens on the D600.
The D600 has more dynamic range, more color bit depth, and better high ISO performance, and more resolution than the D7000.
DX sensors (23,6mm x 15.6mm) are smaller than an FX sensor (36mm x 24mm), DX lenses are designed to project a smaller image circle on the sensor plane. This allows DX lenses to be smaller, lighter, and less expensive than FX lenses because the lens elements can be much smaller in diameter so the require less (expensive)optical glass than an FX lens of the same focal length.
Since FX lenses are designed to project an image circle large enough to cover an FX sensor they will be sharper in the corners and vignette less than a DX lens when used on a DX body. Good Luck and Enjoy your Nikons!