I get quite good battery life with my galaxy s3(i747) with the stock OS. Battery is currently at 39% after 36 hours and at least 2 or so hours of game playing, some web browsing, auto updates on apps, facebook auto updates, gmail, etc.
I have been home the whole time so data is exclusively over WiFi which will explain some of that. I've also disabled LTE and went HSPA only as LTE is sketchy in my area which was causing the Cell radio to cut out as it switched between them(when not on WiFi), not to mention low signal, especially with LTE, is a battery hog.
I've only had for 8 days now so pretty much everything is still at default values, meaning power saving option is disabled, screen is on auto brightness, etc.
And if I go hog wild, I can get roughly 5 solid hours of gameplay or more before low battery warning. Which is a good 2 hours longer than my old Galaxy S Vibrant(i9000m).
One thing to be aware of, is like most Li-Ion battery devices, when the message comes up to say its fully charged, it actually isn't yet fully charged. Li-ion batteries can be quick charged up to a certain point(which is when it says fully charged), after that they need to charge slower to get to full capacity. I noticed that when I took my phone off the charger right away when it said it was charged and ~15-20 minutes later of being off, the charge was already down to 90%, which is when I remembered about the Li-Ion charging pattern.