Disclaimer - I have an iPhone, wife has one and I have an iPad, an Apple TV, and MBP. So my views are going to be somewhat slanted to the Apple stable of products. I never used to be.
I sat down with friend earlier on in the week as he had just got the iPhone 5S and a Galaxy S4 as we write apps together so we need the hardware. So I sat about playing with both that evening. First time to really play with Android (apart from a wifes friends android at the weekend, which was getting a lot of spam messages (not email or SMS's from somewhere) so I was trying to figure out why, her son had put lots a free dubious apps which appeared to be advert messaging her )
They both are bloody good phones, both have merits. At the time I could not really get the eye tracking feature (Android) to work and scroll down a webpage based on my eye movement, but I was in a restaurant at the time so perhaps the lighting was not optimal). Lots of stuff on the android lots a settings to play with. Lovely big screen if that is what you like (personally I think there is a sweet spot on size of phone before you look like a Dom Jolly sketch. Lovely colours. Yes it was different, of course it was different, so it would take a while to get used to. However I did not find Android as intuitive compared to iOS. The new iOS7 although is iterative in its feature set is an even more stylish OS. Very nice on the eye. But hey Android looked good too. Especially with the large colourful screen again!!!
But I would repeat what a friend who switched to Android a year or two back and then came back to iOS. He said if he would recommending a phone to his parents then he would not be recommending the Android. If you want to tinker with settings and customise, i.e. you are a geek, then the Android is best. If you just want an easy life and things to just work then the iOS based device is the way forward. He has switched back to Apple, not least as it integrates nicely in his company car and has an app from the manufacturer that shows him the G's he's pulling as he goes round a corner. And currently he wont go back.
Apple has Airplay so you can wireless send music, video and pictures to other Airplay compatible devices. I not too familiar with Android/Samsungs equivilent. But lets put it this way. With AirPlay you no longer need expensive Bang & Olufsen multi-room systems. Rather you you can have Airplay compatible docks and HiFi systems (most manufacturers have somewhere in their range an AirPlay compatible device) and move from room to room with the iOS device and stream music to your airplay device. Me I have Spotify and I wirelessly stream the music to the phone out to the Airplay device. Awesome. Simple. I can video my kids doing an after school activity and immediately stream it from my phone to my Apple TV to see on the big screen. I know the latter is possible in the Samsung world too.
If you are an Android person. Stick with it. The S4 is a nice phone.However if you want simplicity and style and are willing to pay the premium then Apple is your best bet.
This weeks
Moneysavingexpert.com email showed the TCO on both phones. There was on 1 network a startling £500 difference between the TCO of S4 to the 5S. The latter being more expensive. This may factor hugely for you.
Good luck.
R