I've owned iPhone and several Android devices. The S4 has the best battery life of any I've used. I easily get 10hrs with moderate to heavy use. I suspect the display S4 had auto-brightness enabled (its default), which most people find unsatisfactory. I have it disabled with the slide setting in the middle, and it is plenty bright.
Help yourself while helping me: Sign up with Dropbox and we both get 250MB extra space. Thanx!