I would say James Bond. Because though Jason Bourne is shown highly fast in his fighting skills, and highly smart and very quick in his actions, Bond is more International Spy.
Jason Bourne's stories are limited only to getting out of (and revealing the corruption) inside CIA - and living a normal life,
While Bond is all the time in business, and does more work - He kills terrorists, Ex-Nazis, Extremists, Evil Geniuses, explores and reveals World Mafia Networks, kills Bad Secret Agents, etc...Bond is a Super-Hero Spy.
Jason Bourne is lucky because Paul Greengrass directed it, and all the three films are filled with realism. Which is why Jason Bourne looks more real spy then Bond.
While Bond as we know, is a classic Spy, and has more classic films to his credit, which feels more like a mainstream entertainer movies.
But Daniel Craig series is getting more closer to Jason Bourne series, which means realism can be seen.
Casino Royale changed all that classic mainstream thing attached with Bond films.
Quantum of Solace was little less interesting than Casino Royale - because of the change of the director.
And I'm waiting for 'Skyfall', which again has a good director - Sam Mendes , who is an Oscar winner and has directed films like 'American Beauty' , 'Road to Perdition' , 'Jarhead'.
So I think Skyfall will be good. But more can be said only after watching it.