AFAIK, the power consumption of typical LCD screen is about 75% for back-light. As for pixels, it's not that much about the number of pixels but the area of screen they have to cover. One big pixel can use roughly same amount of juice as several smaller pixels covering the same area. There is some power "wasted" on circuitry needed for handling extra pixels but AFAIK it shouldn't be significant compared to other things consuming power.

Bigger resolutions do need more capable SoC/GPU, which may or may not lead to increased power consumption. It depends on how much newer SoC/GPU has improved on performance AND how that has affected power efficiency on those chips. Moving to smaller manufacturing process helps on this regard, as well as possibility to cram more transistors to smaller die (of course the design/architecture has to be good). So, I do question the idea that older, low powered chip coupled with low resolution screen automatically results in more power efficient device compared to newer chip with relatively high resolution screen if the devices are similar in size.