The really interesting data point to me is the 6+'s 13.7 hours of WiFi browsing versus the LG G3's 8.8 hours. Both are 5.5" screens with ~3000 mAh batteries, but the iOS/A8 combo lasts more than 50% longer.
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.
Someone made a claim that controlling the hardware and software stack was the driver for being able to do well, powerwise.
I'm saying that controlling the hardware and software stack probably had less to do with this performance than the GPU only needing to push 40% as many pixels. I would also bet the overall hardware PM is better in Apple's chips.
Software wise, there is only so much you can do that has any real impact, given that screen is 40% of power and cell is another 20%.
Past that, only real way to save power is often to make stuff run faster.
But to give you some perspective, if you take any of these phones, turn off cell usage and shove them in a drawer, they should last at least a week.
Apple is very good at convincing people of what they want (i don't think they simply give people what people already wanted). In a case like this, IMHO, they could have had slightly better battery life than the 5S, and said "we've packed a lot more power in the same battery life", and people would have likely been fine with it.