I have an iPhone 5. I love it. I upgraded from an iPhone 4 and hubby has a 4S so I can say without a doubt that it's super fast. It's way faster than my 4, which is really saying a lot. The screen is crisp and clear and the phone itself is the perfect size for my hand. If the Galaxy s3 is the one I'm thinking of, it's too big for me. (Honestly, that's all I know about the Galaxy s3.)
My experience with my 5 isn't anything like what Scrills mentioned about her coworkers. Everything on my iPhone is fully integrated--photos, apps, email, contacts, etc. All my songs and photos update automatically from iTunes to my phone, iPad, computer, etc. I've never run out of space on any of my iPhones but that would be 100% dependent on the user. YMMV.
The main thing I like about having an iPhone is that I don't have to deal with my wireless carrier unless I have a problem with my bill. If something happens to my phone or I have any issues with it, I just go to the Apple store and they either fix it immediately or give me a new phone on the spot--no questions asked. I hated the days when I had to call Verizon and have them spend 2 hours with me troubleshooting some problem and then wait for them to send me a phone.