having a smaller display (and possibly downgrading/downclocking the gpu accordingly) saves some power, but the power draw of other components doesn't scale with the size of the screen. the display doesn't account for enough of the overall power budget to offset having less energy to power everything else. it's possible to make a small phone with "acceptable" battery life, but they'll never compete with bigger phones on that front.
btw, apple doesn't have some magical solution to this scaling problem. their small phones have significantly worse battery life than their larger offerings. it's just that their overall efficiency advantage makes a small iphone more viable than a small android phone.