The Apple iPhone 5s is the king of the iOS ecosystem with a new 64-bit Apple A7 processor and a touch ID fingerprint sensor packed in for good measure. It comes in a sleek portable form with an excellent build quality. The Samsung Galaxy S4 takes a different approach trying to pack everything it can under its hood to offer its users a top of its class experience.
Samsung's Galaxy Series is clearly inspired by the iPhone, but has come a long way since. At the end of the day both the Galaxy S4 and the iPhone 5s wont disappoint with great user experiences on the software and hardware side.
You can read a detailed comparison of the Apple iPhone 5s and the Samsung Galaxy S4 on PhoneArena.