First thing I thought when watching their last (and actual first) fight: "Captain America would die so horribly..." Seriously, it is impossible not to compare those "super-humans" from the movie to Captain America, because, despite the original Mandarin using magic and ancient powers, this version of him is basically a regular guy powered-up by biotechnology. The super-soldier was just reduced to nothing in terms of super-human capacity.
As for the question, call me crazy but I think that Batman would have a better chance than Tony did. He'd probably resist as long as he could (avoiding the guy's attacks, for example) and somehow manage to neutralize the Extremis formula.
Which Batman? Nolan Batman? Batman from Brave and the Bold?..
Probably not Nolan's Batman - I mean, we was cool but not half as smart as most of the character's version. I think most "Batmen" could do that, the New 52's is an example.