I wish I had your probelm! 
Well, the 5960 was first launched in 2006, Patek's first totally in-house automatic chrono. it is a very nice piece and sits well on the wrist as do your other two choices. It is an iconic piece. Some do not prefer the way the annual calendar is split over the dial at the 10, 12 and 2:00 position. For me, I don't mind it as much since I prefer apertures over sub dials.
As for the dial colors, I do not prefer the two tone gray dial and vacillate between the blue and anthracite dials. There's something about that blue sunburst dial and yet, that anthracite... ahhhhh!
The pushers are smooth and sporty looking on the 5960 but I prefer the style of the 5980, 5070 or so.
The 5980 has the same movement as the 5960 and half its price~ sans the annual calendar and power reserve. The 5980 is a little more water resistant.
With that said, any one of your three choices will be a GREAT choice but ask yourself this... which one is the one you cannot live without?
Good luck!
Aloha,
Bob