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This is not at all surprising. You are cropping a 24MP image to 10MP, and comparing to 16MP. A much better test would be to resample the D600 images to 16MP. Then you will find the D600 results to be superior.
Depends. If the crop of the 24MP FX images is necessary to get the required and same angle of view (and assuming you can't get that angle of view by moving closer or with more focal length) then the crop and upsample would be the best comparison to the DX.
With respect to DX/FX the trade off is pixels on subject verus pixel quality. There is no correct answer for everyone in every situation. And the skill involved capturing and processing the image will usually mask the difference.
I had also been looking at the D800 and D7100 as replacements for my D300s.
BTW, those holding their breath for the D400 DX camera can now breathe easy as I just ordered a D7100. I'm sure now that I've jumped, it is just around the corner. I waited 4 years for the AF-S 80-400mm f/4.5-5.6 VR II update and upgraded the old AF-D 80-200mm f/2.8 to the AF-S 70-200mm f/2.8 VRII w/ TC-14EIII just 4 months before Nikon announced it!