DX on D4 is 3200 x 2128 D300 is 4288 x 2848 D800 is 4800 x 3200
So you're going to lose resolution substantially but gain in high ISO performance (as well as frames per second, etc.) Bear in mind that a few years ago 3200x2138 was considered a high resolution sensor.
A somewhat more interesting comparison is the D800 which actually gains you both resolution and high ISO, but you lose a bit in FPS (if you shot the D300 at 12bits as opposed to 14bits).
For anything but stationary subjects, however, I think you are better off shooting in FX mode and cropping, as then you are much less likely to slightly miss the action. How often have you just barely clipped the wing on a bird in flight, or the ball was just barely out of the DX frame.
The D4 is an amazing camera, but it doesn't have the resolution some of the DX cameras has. It works well there, but it shines in FX. Thus it will cause a medical condition called NAS which will cause you to acquire longer and heavier lenses.