Obama could beat Boehner in a boxing match because Boehner is 12 years older than Obama and is a smoker. Boehner was a linebacker back in his high school days but is now 64, while Obama is only 52. Boehner is committed to his smoking habit, and has even just recently said he wouldn't trade cigarettes to be the president
President Obama is in great shape (basing this purely on pictures and Michael Lewis' Vanity Fair piece) and could easily beat Boehner in a boxing match. Boehner is also several years older than Obama, and would therefore be at a serious sports match disadvantage regardless of his level of physical activity.
Because Obama is younger than Boehner, he is more agile, faster, and stronger. It stands to reason that Obama could beat him in a exhibition match OR a real one. Another advantage Obama has is that he has better hand-eye coordination. And lastly, Obama has more stamina and is more durable.