I have both an iPhone 5 and a Samsung Galaxy S3 so I can talk from experience. Of course, your mileage may vary so please take what iIsay as merely my own opinion based on my experiences with both devices, rather than gospel truth of how it is across all devices.
The battery on the S3 is woeful. it just will not last a single day without a charge at about 6pm at the latest. I have even bought a battery pack so i can charge my phone when i'm out and about, such is the poor battery life. In comparison to the iPhone, it is shockingly bad.
The S3 looks cheap and plastic compared to the iPhone. Whilst that in itself isn't a problem as it sits in a case all the time, there is torsion there. By that i mean that I can flex the phone by gripping the four corners and moving the diagonals together.
Android is a lot more open than iOS. The functionality of Android is incredible; there are apps that will do anything that you could possibly do on a phone. The downside of that is that as Android is available for hundreds, if not thousands of different phones, compatibility seems to be an issue, at least for me. On a few occasions, I have purchased apps on Google Play that say they work on the SGS3 but in practice actually they just don't work. Whilst there is a window to delete the app and obtain a full refund, i've not always been able to do that due to phone signal or any number of other reasons, so I am stuck with apps that I paid for, that just do not work. The number of free apps is greater on Android but a number of them contain adverts that are just too intrusive, or my favourite hatred, 'push ads'. Ads that push themselves to your notification bar and pop up a box that gives you a fake security warning (for instance). Whilst there are further apps to remove those, it just seems like you are having to buy an app to fix another app, which is silly.
iOS just works. It's not perfect and there are lots of things I wish it did in comparison to Android (Tasker for instance), but iOS is very user friendly and very stable. One of my biggest gripes is that Android just falls over all the time on my phone (I'm running ICS as JB isn't released yet). Many people have said to me "Oh you should root it and run a more stable custom ROM) but to be honest, if in order to get the phone running with any degree of stability I need to do something that isn't recommended by the manufacturer, then there is a major problem somewhere.
Of course, rooting/jailbreaking does open up more functionality but shouldn't required to make the phone work properly.
Android is definitely worth a look if you are into tinkering with your phone, as the options available on the SGS3 with Ice Cream Sandwich are huge. On the other hand, if you want a Smartphone that works with little fuss, then an iPhone is the way to go.
As I said above, these are just my observations based on my own experiences with my phones and should not be taken as any kind of definitive truth on how they are in the wider world.