It's great with the leaked ICS rom, fat? opinion, I personally hate thin phones, I had a One X and it felt like a plastic toy, way too thin and way too light. But that's just my opinion *shrug*
Battery life? The Galaxy has better talk time, everything else is virtually identical. And with the leaked ICS rom the Rezound will surpass it in everything but talk time and video play back.
Screen's inferior? another opinion. The SGIII screen isn't anything special, and as with every other Samsung phone the whites look god awful. But! the blacks are superior so that negates the piss poor whites right? Rezound has poor blacks SGIII has poor whites, if you use your phone outdoors the Samsung gets >. If you use it in doors and aren't running hacked system apps that are inverted the whites on the Rezound will blow the Samsung away. The stock GB system apps are all white, same with ICS. Neither phone has a clearly better screen, it all depends on what you plan to use the phone for. I'm not saying the Rezound has a better screen, I'm saying for what *I* use my phone for it has a much better screen. This obviously isn't the case for you.