Matthew wants to upgrade either to an LG G3 or a Samsung Galaxy Note 4. Leo says both are great options, but they're a generation behind. The LG G4 and Samsung next gen Galaxy Note will be out by March. And if he goes with the LG G3 or Note 4, they may get stuck in Android Marshmallow due to carriers.
Of those, though, Leo says the Note 4 is a better option because he can get a backup battery. Apple may be announcing a smaller iPhone based on the iPhone 5s size called "iPhone 5se.
It would be as fast as the modern iPhones, though, and would cost less.