It's not just the larger screen, but the much higher resolution which requires more processing power and, in turn, more battery.
The battery in the iPhone 6s Plus is 1.69x bigger than the iPhone SE's battery, but the display is 1.89x bigger.
The battery in the iPad Air 2 is 2.67x bigger than the iPhone 6s Plus and the screen is 3.47x bigger.
When you factor in the fact that the iPhone 6s Plus has almost 3x as many pixels to push as the iPhone SE, while the iPad only has about 1.5x as many pixels to push as the iPhone 6s Plus, the numbers seem to add up pretty nicely. If the iPhone SE had a 1080p display, I'm sure you'd see a drastic reduction in battery life.