These are just what I've heard from friends, family, and online reviews since I don't have a smartphone of my own. (Yes, I am one of those retro teenagers who are still smarter than their own phone).
Samsung Galaxy S4
Samsung Galaxy Note 3 (although it has a really large screen)
Motorola Droid Maxx
Sony Xperia Z
Nokia Lumia 1020
All of these had about 6 hours or more of battery life when using it regularly (surfing the web, downloading, calling, texting, etc.). I'm not sure how long your iPhone battery lasts (depends on amount of usage and phone settings), so I'm not sure how these options will seem to you. You can look up more reviews on these phones if you are interested. They're everywhere if you search on Google and other search engines.
I hope these helped!