If you buy an iPhone 5, check it for scratches out of the box.
Make sure you understand the serious shortcomings with the Maps app.
Find out if they have fixed the Wi-Fi connectivity issues.
If you buy a white one, check and make sure that light isn't leaking through the cover around the bezel before you leave the store.
www.spigen.com sells awesome thin cases for the phone.

If you buy an S3, understand that you need to use the back button to close out apps. TouchWiz has issues with 20-30 apps running in the background.
Understand that you will be tied to Google somewhat closely as long as you have the phone.
www.spigen.com sells awesome thin cases for the phone.

I'm a huge Android fan, but both phones have their merits. The iPhone 5 released with some issues that I am sure Apple will address soon. Just know what you are getting into with either phone. www.xda-developers.com and www.phonescoop.com might help with your decision.

XDA has terrible posters. Phonescoop has terrible posters. Take all advice on the Internet with a lot of salt. Mine included.