If find the D4 has features that I am finding that the D800 does not, such as the ability to shoot bracketing at 2 or 3 EV instead of the D800 1 EV max bracketing. Of course, this does not have anything to do with hardware, just software. There is no reason the D800 can't do this except Nikon wanted more advanced featured on the D4 to try and get more buyers.
Of course, there is some hardware differences such as the D4 10 fps instead of D800's 4.5 fps, the d4 has a huge buffer so you can shoot up to 200 images before the camera slows, and excellent AF.
I really like the d4, and as already mentioned, I expect this camera to last years to come.