In a cage match, where it's just straight fisticuffs -- Bourne. In fact, he would win this match quite easily.
In the real world, in an impromptu fight, where they can exploit the peculiarities of their surroundings, and use their wits to find weapons in odd places, Bond wins.
If the fight is not impromptu, but they know the showdown is going to happen, and they can both prepare for it, they would realize that they were actually being set up, and join forces to defeat their common enemy.