I don't know that I'd pose it as a question of which was better, BO or GWB, because I think they were very different types of leaders thrust into very different types of presidencies. I do think history is going to partially vindicate Bush, while basically discarding Obama.
Bush got elected by his father's political machine and was just supposed to sit there as a token president in the Bush Family Legacy. Unfortunately, he happened to be sitting in the Oval Office when two major events occurred that changed American history--9/11 and then, of course, the market crash. To be fair, there really isn't any effective training for dealing with largely unprecedented events. And the Bush White House was, ultimately, controlled by the Cheney/Rumsfeld group as well as his family's business interests.
All things considered, I think Bush handled our response to 9/11 as well as he could have and even today the public agrees. Was Iraq a great idea? No, but it wasn't really Bush's idea. But it was a big idea, and we ended up learning a very valuable lesson from it on when, why and how we should invade countries. Our fuck up in Iraq may ultimately prevent us from trying the same thing with Iran, and if that's the case then I'd have to say it was somewhat worthwhile because, as history has shown, Iraq didn't really have any WMDs but Iran sure as shit does. And nobody had ever experienced what allowing banks to exploit sub-prime loans on such a massive scale could do, so again, a royal fuck up but we learned from it. Our banking systems now have a bit more oversight and regulations are smarter.
Obama was a guy who got to the U.S. Senate by basically being in the right place at the right time. He had absolutely zero executive, administrative or leadership experience and zero business trying to become leader of the free world. But Obama, again, was in the right place at the right time, and he became president for three simple reasons: 1) He gave a good speech, 2) He wasn't George Bush and 3) He was black. And his presidency, unlike that of GWB, was more or less very uneventful. He really wasn't given any big opportunities to fuck up like GWB had. He simply sat there looking and sounding cool while the economy eventually recovered (at the slowest recovery pace in American history), as the existing Bush military strategy was left in place and dealt with resolving our fuck ups in the Middle East (although he campaigned against those strategies and vowed to end them...but never did). I mean, what big events happened in his 8 years? A couple of black kids got shot and he used the opportunity to rile up race tensions and piss off White America. Then Bin Laden got smoked...using the same military apparatus, technology and techniques Obama vowed to end but was perfectly happy to take credit for later. I mean, Benghazi was the biggest geopolitical event of all and he was more than happy to throw Hillary under the bus for that one.
I would have to say that had Obama been put through the same challenges as Bush, given the team Obama surrounded himself with and the political dogma he followed, I believe he would've screwed up far worse than Bush. But we'll never really know. But in fifty years, GWB will be remembered as the president who saw us through 9/11, while BO while be "Who? Oh, that black guy."
And liberals will still be crying about Trump.