For financial reasons I'm stuck with Sprint, but even without an LTE network this phone is fast. I have MLB.tv and watched games on it with no lag issues and great picture quality. I thought the commercials were silly but I actually have used the take a picture from video feature quite often.
Rambling review I know but just typing as I think. I can't speak for the Gs3 but I love what I have.
I originally had the iPhone 4, but decided to get the HTC Evo when it was time for my upgrade. The Evo was alright, but I just preferred the interface on the iPhone and the app store for the iPhone is much better. I ended up getting rid of the Evo and getting the iPhone 4S again because I like the phone much more. I would suggest just getting an iPhone, as most phones are just trying to imitate the iPhone anyway. You might as well pay a little more and just have the best phone possible. This is just my opinion, but I hope it helped.