I just got the newest version of the Nikkor 24-70mm f2.8 VR lens. I tested it out last week, and think that it works very well with my Nikon D800! A few samples taken at 1/30th of a second or more:
Picked up a second hand 17-55G f2.8 DX lens yesterday for a third of the price of a new one. Great bargain and it will be on its way to France in April to live on my D200. No DX cameras here to try it out.
You can try it out by putting your FX camera in DX mode. In fact that may be the default on the FX camera. I think it will detect a DX lens and automatically switch to DX mode.