Like you both cameras came on the same day and I had to choose one. Mostly because I could not afford the D4 but also due to the weight I went home with the D800. One factor is it uses the same battery and SD card as my V1 and D7000.
AnyWay, I kept regretting my decision for the first couple weeks until I started learning how to get the most out of my D800. Some of the pictures from my hikes were absolutely stunning, and the D800 kept up just fine at MotoCross Events (I shoot at 4fps even with a D1-4).
It has been nearly two months now. I had my best shoot ever at last Sundays Equestrian Event. Best pictures and most keepers. This Thursday at the Academy of Science Aquarium I successfully tested the High ISO at 6400. And, the "Home Movies" have been better than anything else I've used including VideoCams.
As for the title of this post, YES But the difference is marginal. All the Nikons I have used take great pictures. For me the D4 is easiest to use and the D7000 is the most comfortable to use. The D800e probably has the most potential of any camera made to date.