Is the d4 better at focusing than the d800?

I think it is enough to compare the manuals or test in shops with the same lens. No need for any scientific experiment or other proof. The D4 shoots faster, is intended more for sport shooters, where high frame rate with AF is important. I think that it is obvious that the D4 AF performance is not the same as the D800, but sure, for the same lens in single shots it may perform equally, though the D4 has also a more powerful battery, which normally also increase focus speed.