Re: Cheaper phone, bigger battery
Yeah, it appear a lot of cheaper phones have bigger batteries. A bigger battery (say 5000 instead of 4000 mAh, 20% difference) can offset the lack of an OLED display, which, according to Google, can save between 15% and 60% power consumption over an LED display when watching YouTube. So, don't go on battery size alone to estimate battery life - find a testing website which uses a test that approximates your use (eg, browsing or watching video) for your existing phone and your prospective purchase.
Naturally it depends on how you use it. It may be that the more price sensitive buyers are younger and thus more likely to play games, in which case the CPU/GPU and not the screen is likely to be the biggest power draw.