I was also a D3s shooter, but there were a lot of times in low light, sports shooting situations, that I had to press the AF-ON button(how I focus)multiple times to acquire initial focus. Once it focused, it tracked fine.
I've shot the D4 for 3 basketball games, in the same arena as the D3s was used, and the AF just nailed it every time. Several times, I could actually swing and shoot another player, without fail. And that was another area that the D3s was just enough slower than the D4 to cause me to miss the shot.
So if you shoot a lot of fast action, in low light, the D4's AF is a big improvement over the D3s....jmho.