Yea if it were up to me, I would have gotten the Galaxy Note II, but if you are deciding here's my thoughts (based on the fact my gf has a iphone5 and I have a Galaxy S3):
-The iphone is a lot smaller, but the build quality is very sturdy. If you have small hands, it'll be nice. You can also text or do a lot of functions with one hand with the iphone. I have larger hands so my s3 fits nicely in my hand, so holding her iphone feels really tiny. I also like the larger screen on the s3, easier for my eyes. I also tend to do a lot and customize my phone so the android system suits me much better than the iOS, which seems to be more intuitive and easier to use for newbies to smartphones. I find that iOS limits my ability to do a lot of things or makes them harder since I tend to do more with my phone than normal people do (watching mkv video files takes a bit more effort to do on her iphone than it does with my s3, but there is a way with both you just have to do more to go around the iOS system).
-The battery life on my s3 is better than her iphone... she actually complains that it loses charge not even all the way through the day. I also can use up most of my charge but thats only if I game a lot or browse sites and watch youtube. I'd say the iphone lasts 8-10 hours while the galaxy s3 lasts 10-12 hours with medium-heavy usage, a personal experience.
-I think I saw a review somewhere, but they mentioned the display is better in the iphone. While I like the displays for both, I was able to look at the tile setup for both under the microscope, I'd say the resolution of the iphone is better (it does have higher ppi) and the color contrast and color reproduction is bettter than the s3. However, the screen is ridiculously tiny for me, so I like having that extra inch or so on screen space so I don't have to look that closely.
That being said I'm glad samsung went with the RGB instead of the Pentile display, as it really made the screen slightly more fuzzy than the iphone display.
-I like having my headphone jack on the top of the screen as opposed to the bottom like the iphone. However I do like the plug for the iphone in that it is easy to put in, however its not a universal plug and chargers are expensive for the iphone. I can get 2-3 different microusb plugs for my s3 for under $15 shipped from amazon.
-I installed a 32GB microSD card for an additional $20, a class 10 sandisk one. You can't do that with the iphone5... I can also install 3rd party battery pack on the back of the s3.
there is google maps on both now so thats good for iOS users.
Anyways I guess its all on preference really. I like android system and I really like the style of the samsung smartphones (galaxy s3 and note II) and most likely will get the s4 if it has the specs I'm thinking it will have from the rumors. You may want to wait a couple months to see if you want to get the S4 or iphone 5S.