What I'm going to say has applied historically to the 5 Nikon camneras I have shot. The specific performance of the D600 will have to stand the test of time as wildlife photographers use it. You might get a hint from D7000 shooters since that is probably the closest AF engine in a camera that has been out there for awhile.
In general, the fewer focus points that a camera is watching the more attention it pays to each focus point. It has finite processing power and when using multiple focus points that finite processing power is "multi-tasking" each focus point.
The above suggests that the most accurate focus is achieved with a single focus point.
If you are tracking a single bird in flight then you may not be able to keep that single focus point on the bird. If you can't then you lose focus entirely, rather than maybe getting marginally worse focus with 9 or 21 point dynamic focus, for example, on my D300 and D700.
Because the right number of points to use depends on your skill only you can find the perfect happy medium.
I generally use 9 focus points for BIF because I know from experience that one is not enough, and 9 is usually enough if I am on my game.
I have no opinion on the relative efficiency of the D600 when used with the various clusters of focus points and at this point I doubt anyone has enough experience with this type of work on that particular body to come to a firm opinion.
When I shot the D200, which is very similar to the D80 in focus setup, I also tended to use it with "large" focus sensors. When I got a D300 and then D700 I always used the smaller sensors, and 9 pt with tough moving subjects.
I'm not sure now why I used the D200 with large sensors. But I did not shoot a lot of BIF with it. I used a D2h for that. With the smaller modern sensors I like to have a smaller "focus target area" to make sure the camera is focusing on what I think/hope it is. The larger sensors can pick up unwanted subjects at some other distance.
If, for example, using larger sensors on the D80 you might want to change to the smaller sensors only if your images are sometimes mis-focused because the larger sensor grabbed something other than the precise subject you were aiming for. That principle should apply to the D600. So again, your images will tell you if you need to change strategy and settings.