As Steve Benen said earlier, there’s little risk that the full historical record will wind up showing George W. Bush was more focused than Barack Obama on going after Osama bin Laden.
But to reformulate this a bit; it’s still not the case that the campaign against bin Laden began in September 2001. There’s a reason that Obama called both Bush and Bill Clinton yesterday. It was under Bill Clinton that al-Qaeda became a deadly threat to the United States and its allies, and it was under Bill Clinton that the war on bin Laden and al-Qaeda began. The real anomaly, even more so that the massive Iraq distraction, was the well-documented decision by the incoming Bush administration in January 2001 to downplay the threat, and to genuinely believe that September 2001 was the beginning of something. Granted, it was in his political interest to convey that idea, and one never knows what politicians really think, but I believe Bush on that one.
Barack Obama, in my view to his credit, does not seem to have taken that same attitude toward his predecessor, who of course left office with terrible approval ratings and worse assessments by scholars (including, well, me). I’m not really talking about specific policies; it’s natural for incoming presidents, especially those from the other party, to attempt to implement the policies they campaigned for, which generally are going to be very different than those of the outgoing administration. It’s more a basic attitude. We’ve read that Bush reflexively rejected whatever Clinton was doing, while I’m not aware of any similar stories about Barack Obama. Indeed — part of this story was about a well-run military under Defense Secretary Bob Gates; can anyone imagine George W. Bush having retained a Clinton cabinet member? No chance. Part of what makes Barack Obama far better at the job of the presidency than George W. Bush is that he appears to be willing to make use of whatever resources, and whatever sources of information, he can find.
Update: Via e-mail, excellent fact-checker Glenn Kessler points out that indeed, George W. Bush did carry over a Clinton cabinet member: Norm Mineta, who moved from Commerce under Clinton to Transportation under Bush. So I guess one can imagine it! I think the larger point still holds, but my apologies for the error.