I'm debating the same thing right now, so I'll give you my thoughts. I've played with both extensively. As a note, I am not an iPhone fan at all, in fact, I resisted even considering it.
S3 - Pros *Android OS, soon to upgrade, more customizable *Bigger, prettier screen, very responsive *SWYPE! *Free (mostly) apps, almost everything you can get on the apple store
S3-Cons *Fails drop tests, repeatedly *My hands are tiny, and it's a bit uncomfortable *Cases make it huge *Getting to the 'phone' to make a call requires way too many buttons *The music player absolutely blows *The screen is almost too sensitive, it responds to things and you end up on a screen you didn't mean to
iPhone5-Pros *iOS is easy, integrates with almost everything these days *Hands down best app store *Great screen, responsive and pretty *survives drop tests, they seem to have figured out how to protect the screen! *Extensive case options that are small and protective *Everything you already own for iPad will be avail on iPhone *It fits in my hands much better *I personally feel like it is more of a solved problem, seems more reliable, solid. S3 seems like they're still working out the bugs
iPhone-Cons *I feel like a sellout/sheep/lemming/etc *I hate the fact that it has a special connector - so if I need more than 1, it's another $40 or something stupid *It's more expensive (for me, plans may vary) *iOS is not as customizeable
Unknowns: *Call quality *Speed of internet/downloads in my area (no LTE for Sprint here, and I'm not leaving Sprint) *Longevity
Result: My phone can be replaced on Nov 1, but if I could order it today, I'd order the iPhone 5. If you asked me a week ago, I'd have said SG3, but that was before I'd tested an iPhone. Ask me again in a month!
I love my S3. It's not perfect (and certainly neither is the iPhone) but I don't have any substantive complaints about it. I like the screen size, the battery life is great (today is day 3!), call quality is great. The Android app store is getting better every single day. The texting swipy thing is amazing. I don't know how I texted before without it.
And the camera is AWESOME. I don't think I'll ever have to buy a digital camera again.
iPhone 5 has an aluminum (and plastic?) back now, no glass. The iPhone seems to survive landing on it's edges now, where the glass on the S3 breaks more easily when it lands on an edge.
I HATE Android phones - both H and I have them. I had the first iphone, replaced it two years later with another, then switched to a Droid because I wanted 4G. Huge mistake and I can't wait for my upgrade to come (January). The iPhone is very intuitive and easy to use and I feel like nothing makes sense on the Droid. It freezes up on me a lot (ESPECIALLY the camera) and the navigation is awful IMO. They might be better for people who are more techy, but in terms of ease of use the iPhone is much better.