I have a Samsung Galaxy S3, which I love, but honestly, they're both great phones. It comes down to... what do you want?
With iPhone, you get the more polished devices. Apps go through more rigorous testing and are less likely to mess with your phone. An overall more polished experienced, and yet it doesn't give you the same amount of control of your own device.
With the Galaxy S3, you get the premium Android phone on the market. It's big, and sleek, and smooth, but it's still not quite up to the same polish as the iPhone 5, and it's not going to give you the same battery life, either. But you can do things like root it and install your own operating system (CyanogenMod is the gold standard), do off-the-grid tethering and other geeky .
It really comes down to what you care about: longer battery life and a more polished experience with a bigger app store, or a phone with a nicer screen, more customization, and more geeky stuff you can do with your phone?
For most people, an iPhone is probably the better choice. For a geek like me, though, I'll always lean Android.