I would guess that Obama gets the benefit of the doubt because he's trusted.
There are no two people in the United States who are less trusted that GWB and Dick Cheney. It didn't start that way, it started out that folks trusted them, even gave them the power to wage war "if necessary". It wasn't necessary, the American people were betrayed and knew it and it was downhill from there. The continuing betrayals, the unending lies eroded whatever trust rational people had.
Obama hasn't betrayed the American people. And whatever God Obama does involve in his life hasn't led him to declare an unnecessary war.
That counts for a lot. Bush had it, threw it away.
Arf