I had a D300, then a D800, then a D4. I shoot with both of the latter.
If you can buy a D4, you can clearly buy a D800. You should at least ask yourself which does the most for you.
The D4 is fast, and a huge buffer. If you need high speed bursts, no question. It is also a bit better at high ISO.
The D800 on the other hand has a better sensor, at least it has better dynamic range at low ISO, and clearly better resolution. It is slow at 4fps, and it's buffer is not very deep (17-20 depending on cards).
Airshows, wildlife I'd take the D800.
Motorcycle racing and action shots of airsoft - probably the D4. But depends on how important the burst is.
I love the D4. Don't get me wrong. But as I wrote in another thread, I just went on vacation with both D4 and D800 in the bag, and the D4 never came out once; the D800 just takes better images. Yet shooting sports the D800 gets very little use.
I mention it because you will never regret the D4, but if you are only going to get one, you might take the D800(E) and some more glass (you can never have too much glass, despite what my wife says!).