While the iPhone 5 is a really nice piece of hardware and I do admire that Apple has finally admitted that a larger screen is what consumers want for the most part, I am still an Android user through and through. I would definitely prefer the Galaxy S3 over the iPhone 5.
Feature for feature the Galaxy S3 has much more to offer in a thinner package and a much larger screen. It also has NFC (near field communication) which is useful for a great deal of things such as virtual wallet, file sharing and much more.
I've not had bad experiences with my battery life on my phone at all and neither have my friends that own one.