The S3 seems to have developed an issue where the batteries are exploding close to the charging socket. Not enough cases yet to say if it's a design flaw or just a few odd occurrences that aren't statistically significant. That said, the difference between an iPhone and an android phone like the S3 is like the difference between night and day. iPhones are great for people who want a gimmicky device that'll work out of the box but never be much better than that (even when it's jailbroken) - not to mention the fantastic proprietary connector, the inability to drag/drop files or use it as mass storage, and the fact that you need iTunes installed and can only sync with one computer/install of an OS (if you format, you basically have to wipe the iPhone next time you sync, even though it's the same physical PC).
Android phone on the other hand - standard micro-USB interface, usable as mass storage, interfaces through windows explorer, no need to install any extra junk if you don't want to. When rooted and bootloader unlocked, device is capable of some amazing things. Custom ROMs are available for a variety of different purposes - some are geared for gaming, others stability, even others battery life. Easy to use and understand, far more stable (iPhones like to lock up from time to time and it's hard to get it to reboot), far more customisable. The list of advantages goes on and on. Also, Android as a platform is OPEN-SOURCE meaning that anyone can take it and modify it and develop for it - unlike Apples closed-source platform that only they can redesign. Additionally, the rules for the Google Play store (previously Android Market) are made clear and documented, whereas the rules for the Apple Store are vague and largely unknown.
My advice is go for an Android phone. You won't regret it. My starter one was an Xperia X10, I then went to an Xperia Play and have recently upgraded to a Galaxy Note. It's been awesome the entire time.