I've posted this at least ten times in other threads, but hands down, for me, it's Quantum rom by Pwncakes193.
This rom is extremely stable and the developer puts a lot of hard work and time into it. If you try it and like it make sure to say that someone pointed you over there
Oh, there's just one thing you can do for even better batter life, disable ROMdB Dev Tool which is a built in app that gives you notifications when a new update is available. For one reason or another, it can have a negative effect on battery life, so it's usually best to disable it and just check the forum for the updates, plus since the updates are up before they're pushed through the OTA updater. And for Google Settings turn off location reporting and location history.
Rooted AT&T Samsung Galaxy S III running latest Quantum 3 RC5
This phone runs smooth like a red-hot knife through softened butter!
Please hit Thanks if I've helped you in any way or just amused you!