Both phones have plenty of "juice" (read: power) to do whatever you need. I've got the S3 and it is incredibly slick and fast. I came from an iPhone 4, which I was happy with as well. Being an IT guy, I try to get as broad a variety as I can with tech, so I switched to the S3 on that idea alone.
I'm very happy with my S3. I was very happy with my iPhone. It really comes down to whether you feel more comfortable in Android or iOS. Tinkerers will probably like Android better. Folks who like simplicity and a controlled environment will like iOS. It's just a matter of preference.
No one suffers a victory like Gator fans.