I'll abstain from voting, but I'll give you my honest $0.02.
I have the iPhone 5, i absolutely adore it. My wife has the Galaxy SIII. I love my wife's SIII as well, but she doesn't love my iPhone 5. What I'm getting at is the SIII is an amazing phone, but the iPhone 5 is something that you really have to think hard to justify it over the SIII.
My justifications for buying the iPhone 5 were:
-Aesthetics, i felt it looked better
-Size, the SIII was too large for me to use comfortably, funny enough my wife loves it.
-Proper color saturation and crisp brightness on the iPhone over the SIII
-Simplicity, I wasn't interested in learning a phone, the iPhone hardly has a learning curve
-I enjoyed my first gen iPod touch when I bought it way back, so I figured I couldn't lose with the iPhone 5.
Again, these are just my personal preferences and are in no way intended to sway your opinion. It's not quite as simple as asking the forum board which you should get. I spent a good 30min with each phone at the store (actual display models, not dummies) and decided the best fit for me was the iPhone 5.
To be honest though, I have no buyer's remorse whatsoever, but the SIII paired with Android is one heck of a phone, I definitely try to take advantage of every chance I get to fiddle with the Wife's SIII... and it has expandable memory which the iPhone 5 does not.