I'd go with the iPhone 5 personally, Kesa.
I got a S3 recently, and while I do like the thing, I've found the wifi on it to be erratic at best. Randomly loses authentication and passwords and randomly drops off my wireless networks, and it's not an operator error issue, lol. I find the Android settings mechanisms on the handset to be overly complex compared to the iPhone. GPS on my old iPhone was better as well. Apps selection is pretty comparable, but I find Android "free" apps to be so burdened with crapware and adverts they are often unusable. I find the iPhone "multitasking" superior to Android as well.
Having the Google ecosystem crammed down my face on the handset is a little unpleasant as well, but so is the iTunes/Apple walled garden ecosystem.
I dislike the TouchWiz UI a great deal. When I initially got the phone, I liked TouchWiz, but now that I've got used to it I find it infuriating. Many of the Samsung add ons like S Voice are just absolutely useless, and I thought Siri was flaky. I'd be far happier with a vanilla ICS or Jellybean install on the phone, there's just too much crapware you can't get rid of with the Samsung UI. Battery life is terrible as well, but that's more likely to be a LTE/4G wide issue itself. Chances are I'll be trading this phone in for an iPhone 5 in the near future unless I can get a vanilla Jellybean or even ICS install onto it.
While it's a very nice phone (S3) hardware wise, it is a little cheap feeling and I likely would have dropped it 10 times over if I didn't get a rubberized back bumper case for it.
The Samsung Kies sync software leaves a lot to be desired as well, but there's plenty of gripes with iTunes as well. Kies uses extortionate amounts of memory.
It's a good phone, but all in all I still think I prefer my old iPhone to this S3, and I'm by no means an Apple loyalist. Pricewise I could have bought the new iPhone for what I paid for this, and I am beginning to wish I had. If I had to buy another Android phone I'd likely buy into the vanilla Android Nexus from Google to avoid the TouchWiz/Samsung UI trainwreck.
Being able to replace the battery and add a memory card is a big bonus, though, will never have that option with an iphone.