The LG G3 has a 1440x2560 QHD screen. It takes more power to dive more pixels.
Obviously power is more complex than just that, but seriously Android's reputation for being inefficient is really not justified due to things like this, where resolution differences are completely ignored.
Certainly the GPU on the iPhone 6+ is going to take more power because it's rendering at 1242x2208 rather than 1920x1080, but that's a minor effect compared to the physical screen power draw.
That very much IS most of the overall power budget. That was very not a guess on my part.