What does the Galaxy S3 have that the iPhone 5 doesn't?

List like, everything different.
Although personally I think Samsung totally copied the iPhone.

Well, I don't think they "copied" iPhone, but they made something to compete with the iPhone. Now, about the different stuff, nothing much.
The differences are:

iPhone got faster Internet (without Wi-Fi)
The S3's display is larger then iPhone's (S3: 4.8" iPhone 5: 4")
S3 got a higher screen resolution (S3: 720x1280 iPhone 5: 640x1136)
S3 has a faster processor (S3: 1.4GHz iPhone 5: (about) 1.02GHz)
S3 has a microSD port, the iPhone 5 doesn't (which means the S3 can expand its storage space)
They BOTH have 8MP back cameras

So, these are differences I could find.

It doesn't really have any new features, just different features, such as a bigger screen and different design.
The only feature i can think of is the Android OS itself and the smartstay feature.