while I don't have experience with the SIII, I do have the SII. I have been using it for about 6 months. And a former iPhone user. My main reason for switching was the bigger screen.
my thoughts on the two:
OS - prefer by far the iOS. just everything more fluid, and even on the smaller screen, found I could type faster on the iphone.
Build - the SII looks and feels cheap. like another toss away electronics when I'm done with it. While the iphone really seems like a solid device.
voice calling - both works fine and would call it even between the two.
Apps - while i could always find new (free) apps to download and try on the iOS, every time I look on the android market, nothing to enticing or any wow factor like I have found on the iphone.
texting - I love the voice texting on the android, but I am not a huge texter, so while its nice - I wouldn't stay on the android system for it.
Screen - this is my biggest plus for my SII. I love having a bigger screen and at the time really wanted the Samsung Note, but didn't want to pay the price. I read alot on the phone (mostly news), and the bigger screen made it much easier.
One quirky thing, when I zoomed on my iphone, it went perfectly to the block of text I tapped, fitting it perfectly to the screen. On my SII, i am always having to zoom in or out to what I want to read.
Crashes - my SII freezes all the time, mostly browsing, sometimes on a few apps. I always just wait it out, 15-30 sec, the app is forced shut and I relaunch the app (don't necessarily restart the phone). But just an annoyance that seems to bother me more lately.
Would I go back to the iphone, since I have awhile on my contract, who knows what will be out in that time. But the Android OS sure does need some work, stabilization.
I even catch myself using our ipod touch at home on our wifi for some apps instead of using my SII.
Not sure if either phone is perfect, but that is more dependent on the user than the phones themselves ultimately since we all have very different needs.
like do you really want to 'bump' phones??? who was demanding that feature???