Jason Bourne's identity was created solely to draw Carlos the Jackal out. He was given the training of an assassin and any time an assassination by a smaller group or lesser known individual happened, Bourne would claim credit for it. I think Bond is less an assassin and more of an agent that investigates and then takes down the bad guys.
Also, from what I've seen, Bourne (Webb) speaks more languages, has more underground contacts, and can go to ground better than Bond can.