Wait...you only get 3.5-4 hours screen time on a razr maxx?
How?
I can easily hit 4 hours screen on time on the S3. Easily. ( Using lots of browsing with wifi, moderate games, text messages and such. CPU power saver disabled as I want my phone to run to the max. )
I think the only time so far I have managed under 3 hours of screen on time is simply because I didn't hardly use the phone the entire day, but managed to have a wakelock for half of it. This resulted in something like 14 hours since charge, like 2 hours screen on, and 20 some percent left.
heck, pretty sure I could hit 3 hours of screen on time on my OG Incredible with it's pitiful 1300 mah battery which is getting quite tired at this point.
You might want to look and see if you have something going wrong. Bad app, excessive syncing, a particularly nasty live wallpaper, etc.
Also: It doesn't sound like you really need to change to an S3. It sounds like it would be a bit of an overkill for you. Sort of like buying a Bugatti Veyron to go to the grocery store
If you do switch though, it has indeed been a great phone so far, and we'll all welcome you over and help with the transition.