If I were shooting indoor sports in questionable lighting conditions, I would get a D4 or D3s before I would go with a D600 or D800. Your ability to have lower noise images at higher ISO is more critical than overall resolution. The higher burst rate may also be desirable.
I have no qualms shooting my D3s at ISO 6400. I have shot and gotten decent results with more post processing at ISO 12,5000 or 25,000. I cringe at the results with my D800e at anything over ISO 3200, and prefer to keep it below 2000. I don't have one, but my guess is the D600 may be slight better than the D800.
As for the 70-200mm f/2.8 lens, some people, including me, were bothered by the vignetting on the V1 version mounted on an FX body. Others are not. If you already have the earlier version, try it on an FX body before you spend the money on a upgrade.