I ask this because I just got my S3 last week, and I have the battery drain problem really bad. I've found that turning off wifi and mobile data before I put my phone to sleep largely fixes the problem, but that's stupid. I didn't buy the best phone on the market to have to do stupid stuff like that. I will probably put a custom ROM on my phone at some point in the future, but this is my first smart phone ever, so I want to experience the stock ROM for a while just to ground my experience with smart phones.
edit: Woops, I posted this in the wrong Q&A. I meant to post this in the AT&T one, obviously. You guys can still answer I guess, if you want. If a mod wants to delete this or move it, I would be ok with that too. Sorry.