iPhone 5:
For those who want to run basic functions as easily as possible, be able to translate files and operations without skipping a beat, and have the guarantee of one of the most trusted brands in the world, the iPhone 5 is your best bet.
Galaxy S4:
Now if you're into socializing, multitasking, customizing, gaming, pictures and videos, I'd recommend S4. Not to talk about the advantages that you get from installing a custom room which takes the device to it's fullest. Still, even without a custom room you'll never use the hardware to the fullest. There's not even any game yet that can compete with the hardware.