Actually it would be the opposite, the Galaxy S 3 is more efficient because the battery is powering a larger screen, shrink the screen down to the iPhone 5's size and the battery would last EVEN LONGER.
So these are assumptions since you haven't used these phones yet? I have a Galaxy Nexus with the same screen, difference size, 4.65 vs 4.8 at 1280x720. The Nexus has a 2000 mAh battery and from personal experience, the Nexus is no competition when it comes to efficiency against my 4S for battery life, and I'm not even using the Nexus to it's full potential because I'm worried it will die by the end of the day (haven't used it for games or music regularly during the day) while I can do anything on the 4S and be confident it'll last the whole day.
The iPhone 4 was a different ballpark, it's battery life was better than both the 4S and Nexus.