The display and the CPU are going to be your biggest drains on the battery. If you are playing a game or browsing the web, then your system is demanding a lot of energy.
So far, the battery life on mine has been a dramatic improvement over the Galaxy S. With the Mesmerize, I couldn't make it to lunchtime over 50%, and that was sitting idle. Any use at all and it would be nearly dead by lunch.
I'm using my Galaxy S II off and on for calls and texts throughout the day, minor web browsing and app usage. Usually around 60-70%(ish) at 5:00 pm. Coming off the charger at 6:00 am.
I've had one or two days of moderate-heavy usage for 12-14 hours, and drained it down to 15% on those days.