Nikon and Canon have two different visions of how an AF system should be and function, and with what parameters. There are differences in response, starting up , stopping down and loops to hit the target in different scenes. Canon have chosen for example up to f-5, 6, Nikon to F-8.
It would take a very long time to test out which of the systems is generally best, it is probably not doable.
There are reports that the Canon's AF seems faster but the number of keepers at moving subject is greater in Nikon, after some time when colleagues have tried out made we usually emerge which camera produces the best keepers in similar situations, as it emerged with 1dmk3 and d3
First off, the D600's AF system is NOT the same as that found in the D4 or D800. The d600 only has 39 af points, which is essentially a "revamped" D7000 AF. If you look around enough, you will
I primarily shoot sports so AF is critical for me. That being said, a few weeks ago I was shooting volleyball alongside a D4 user. He was switching between his 24-70 and 70-200. I was using my 5d3 paired with my 70-200. When reviewing photos between plays he kept complaining that his D4 kept missing. Mind you this is volleyball, which is a hard sport to shoot in and of itself. However, even for the simplest shots i.e. when the players were serving (nobody else in the frame), his D4 had trouble locking on.
Nearly all of my shots were keepers. Anything I missed was simply user error. I find myself having a hard time in post-processing because its hard to pick out which ones to keep and which to delete.
Shooting through the net, my 5D3 had no problem locking on to the players. His D4 on the other hand, not so much. And from what I keep hearing, Canon's new 61 AF system just works and does it brilliantly. The D4 on the other hand works, but doesn't do anything extraordinary.
On another note, the D600 is capable of shooting sports. I met a guy who had a D4, a D800, and a D600. He was testing out the D600 to see its capabilities as a backup sports body. He seemed to be happy with it. However, he was NOT happy that it did not have a dedicated back-button AF.
The d600 was too small small for my hands (even the 5D3 is a little small for me) and I never liked the button layout/ergonomics of Nikon bodies. The 5D3 is thicker and feels much beefier in my hands. The grip on the Nikon is too small and narrow, which makes my fingers feel very cramped.
Somebody mentioned earlier that people who've used the systems long enough prefer one over the other simply due to ergonomics. I've had my fair share of uses of Nikon bodies and they just don't feel right in my big hands.
Both systems perform so similarly in real world situations (stop oogling over the specs) that it doesn't really matter which system you use. I'm pretty sure that before whatever new camera came along you had absolutely no problems getting the necessary shots.