The Razr Maxx HD will always have the best battery life because its fricking huge. Also the battery life on the way the phone was set up, and how you use it. Even the Maxx HD won't last through a day if you don't stop playing with it. My phone with a lowly 1200mah battery can get me through 6am to 8pm without issue and I already use Facebook, Twitter, calls, SMS and game on that.
Furthermore, the S3 uses AMOLED technology. With proper setting up, an AMOLED screen will use up up to 30-40% less power than a regular LCD screen. Even more if you keep a predominantly black theme.
Also has been said before, you need a proper standardized comparison to see how bad is the battery life of one phone against another. You can't compare one person's usage pattern against another person's. I have a classmate with the exact same phone as I am, but his battery lasts longer because he doesn't have a data plan and thus has his data off always, while I have mine always on. The data service is a battery killer. You need to get an SIII and a Razr HD and make the exact same setup on both and wait them out to get a fair comparison.
So far, I haven't seen a standardized test for the Razr Maxx HD for real life usage, so I won't really comment. But an SIII can last you 3-4 days with minimal usage though. My friend works as a paramedic, and had once left her SGS3 in her locker for 3 days on standby. When she came back it still has 30%.