Some good views in this thread. It's quite nice that many people are giving Android the respect it wasn't getting two or 3 years ago.
I've just bought an S3 after owning a HTC Sensation for a year and a 3GS for two years previous to that. The 3GS was a great phone, by far the best at the time. I then moved onto the Sensation which in my opinion was better than a 4/as good as a 4S, however there were still some reliability issues with the software (which I fixed by flashing a new ROM on but I can't deny they were there beforehand), having said that I had issues with my 3GS back in the day (randomly turning off, got WSOD and had to claim on insurance).
Now I'm just got the S3. Wow, I will say that I've not been this happy with a phone out of the box, period. My mate asked me when I'm going to root it (I'm a fan of tweaking, ended up JBing my 3GS and rooting my sensation) and I've told him that I really don't fancy it! It just works extremely well right now! I had swapped phones for an hour with my brother in law the other day with his brand new ip5 and afterwards he said he was going to ask O2 if he could swap it lol. The ip5 to me feels tiny, the screen is just way to small (smaller than my year old sensation) which is a big thing for me.
As people have said Samsung still aren't building phones as quality as Apple are, they are getting better but still not there. The quality of plastic on my S3 is great but the phone is too light really, too easy to lose grip of. Not a big fan of the power button on the side of the phone either but that's a personal preference.
Fact is you're never going to get an iPhone and think "god this isn't smooth at all" or "this isn't a pleasant user experience" because the UI is so established, and you won't return a good value from a non-Apple phone a year later, it you won't get better build than Apple. BUT, if you are a after a great phone with lots of innovative features then the S3 will never disappoint you, especially with the imminent release of Jelly Bean. I love the things like the bigger screen, auto-panorama images (yes, that did exist before iOS6, and refreshing updates to the OS's which is inherent with Android).
Go for either one and you won't be disappointed.