In the everlasting battle between iOS and Android, the stakes are getting high, in price that is. There has been the all-to-famous lawsuit that Apple filed against Samsung for its voice recognition software, only to end up having Samsung file their own lawsuit against Apple. Well, on that front, the verdict is in. Samsung walks away smiling. They are allowed to sell their line without any payout to Apple. Basically, the Galaxy S III did not take away from iPhone sales, so there you have it.
Now, as for which is better, it all depends on who you are talking to. If you don't mind being married to Apple's proprietary software for the rest of your digital life, then iPhone might be your thing. If you don't mind the occasional bug and early adopter format of the Android OS then looks like you might want to snag the Galaxy. They are both screaming fast and super lightweight, but when it comes to screen size and camera performance, the Galaxy looks to have the upper hand.
As far as Apps go, Apple is killing it. While no-one could possibly use all of the apps on either platform, Apple has made it a point to keep their inventory quite a bit above what Android has been able to do. So, if your just the average Angy Birds player, either phone will suit your needs.
Remember, no matter which phone you go with, pick up a otterbox or some other gnarly protection device to keep from ending up with a broken piece of amazing technology.