Cant speak about the Note 2 much but its a bit too big, AMOLED screens suck IMO and it has a very low ppi count. I have had the S3 since launch, still have it actually but I have been using the iPhone 5 since Oct 31st to try it out. Pretty sure I will be keeping the iPhone 5 and selling the S3. I will give you some detailed reasons rather than just give you a random answer. As a long time Android user, I got tired of my phones always being 1, 2 or even 3 updates behind and all the carrier bloatware on my phone. With the iPhone 5, I have the newest version of the OS as soon as its released and zero carrier BS.
I like the way the iPhone integrates with all of my other Apple products. I like the way it will display the artist, song and album on my car stereo head unit when I have my iPhone connected to it. It also charges it. I prefer the photo and video quality to any of the 8 Android phones I have owned. Its especially good at concerts from an audio standpoint. Apps like Facebook, Twitter and Instagram are faster and higher quality on iOS. Then there is the reception, GPS and overall speed. My iPhone 5 gets better reception than my S3, the GPS locks faster and overall is a much faster device. the iPhone also has a better earpiece, speakerphone and overall build quality. Its also thinner and lighter than my S3.
So what about the S3 do I prefer over the iPhone? Having widgets is cool. Expandable memory via an SD card slot is great. Quick toggle access to wifi, bluetooth and other settings is great. The larger screen is nice to have although I prefer the quality and colors of the iPhone's display. Being able to drag and drop files and songs onto the S3 is much easier than syncing thru iTunes for everything. Both phones and systems have their pros and cons, I am leaning more towards keeping the iPhone 5 though.