Having experienced most iterations of the iPhone (2G, 3GS, and 4) and an early version of android (nexus one), I feel compelled to summarize my iphone experience that eventually led me to the Galaxy S3.
Hardware quality: iPhone has always been the benchmark(iPhone>any android)
Performance: Seems like iPhone 5's performance is off the chart, so Apple can have this one. But the Galaxy S3, with 2GB of RAM, is no slouch
Screen quality: I find iPhone 5's IPS LCD display to be high quality, but the S3 AMOLED's true black is quite easy on the eye. I call this category a draw
iOS vs Android: Android has always had more features, at the expense of ease of use. But recently Android has also gotten much more sophisticated than iOS, and just as intuitive in the recent iterations. With iOS I feel stuck in a icon-based UI dated from 2007, while Android (if Samsung is kind enough to develop the updates) feels like a continuous evolution in user interface.
Google integration: Android wins obviously. Fully integrated Gmail, youtube in HD, full-feature Google maps, Chrome etc leave iOS-associated core apps in the dust. I wish Google would share more of these core services on iOS, but for now I will have to go with Android. Sure Apple has iCloud, but it really is quite primitive compared with Google's offerings.
Overall experience of moving from iPhone to Galaxy S3: Galaxy S3 basically patched up all the inadequacies I saw in my first Android. The UI is silky smooth like iOS and no longer stutters like the N1. Battery life on S3 seems to stand out from your typical android, and is about as good as any iPhone.
Best of all, I feel that the S3, more than any other Android phone, is a successful but shameless attempt to copy the iPhone experience: the round corners of the phone, the single physical home button, the Springboard like app layout. In short, the familiar iOS-like interface, mated to the powerful Google features, were too difficult for me to resist.