I have an S3. DH has an iPhone5. We're both happy with our phones.
Size was a big part of the decision - I don't own a tablet and carry my phone in my handbag, so I wanted a big screen. I actually regret not getting the Note. DH on the other hand wanted a phone he could carry in his pocket and use with one hand, so the iPhone5 works for him.
He likes the ability to synch all his Apple products. I haven't felt that I'm missing anything - I use Dropbox and Google Calendar and Gmail.
I don't think you can go wrong with either phone.