What i think it does better could be completely irrelevant for you though, which is why i said you should probably check out the iPhone 5 and make your own judgement. What i personally feel the iPhone does better is pretty much everything...i don't care for the Android OS at all, i feel it's gimmicky, sloppy and in many ways, cheesy. The phone's feel cheaply made (lots of plastics, loose pieces for various inputs and what not, battery doors, etc), they don't seem to be integrated with any particular control or balance, where as the iPhone combined with iTunes feels more stable, fluid...and the materials the iPhone is made of are (in my opinion) far superior in fit and finish.
Better camera function, faster performance when compared to the competition, better screen picture quality...and in the end, I'm happy with the iOS environment, i know it, it's familiar but also satisfying at the same time.
Now I'm sure there are arguments against this stuff from the Galaxy S III loyal...or just android fans in particular, which is why i refrained from going through this stuff and simply offered the idea of trying it for yourself. You may not agree with anything i said above, and truly, i could care less because what you like doesn't matter to me at all. Hopefully, if you find the iPhone is a better fit for you, we could find a common subject matter to have nice discussions with on this forum, otherwise, enjoy your Android!