I have an iPhone 5 and it's very nice because it is so compatible with everything. There are tons of more phone cases and other things like that which are compatible with the iPhone 5. Also, it's name brand and includes the app store, itunes, etc etc.
Galaxy s4 is much much much faster and has a bigger screen. iPhone 5 has a better camera and larger app store. galaxy s4 has flash in the browser to play games and watch movies for free. iPhone doesn't. id go with galaxy s4.
Samsung GALAXY S4 it is so much better than an iPhone it is bigger better screen better Camera better system better everything get the S4 the iPhone 5s will be out soon and if you get the iPhone 5 you will not be happy