My prediction:
Bourne would snap Bauer's neck after a huge cross-city brawl of epic proportions like when the Chicken brawls with Peter in Family Guy
But then, out of nowhere Chuck Norris would arrive and a third fist that comes out, literally, from his beard would smack Bourne by surprise and he too would die from the knock out blow.
snip
Bauer would not win simply because he's not as fast as Bourne, watch them fight in side by side windows.