I agree get the 1920x1080 screen.
1) I believe there is still SOME increased power draw, possibly just due to the GPU itself processing more pixels but it's hard to guess since it depends on the hardware. Probably not too significant in a modern Intel iGPU.
2) No guarantee both laptops have the same battery life.
3) Backlight as said (AFAIK) is by far the biggest drain so adjust the Power Options so the brightness is the optimal balance of "bright enough" vs battery life.
4) By "heat" I assume you are referring to EXHAUST thus fan noise? I ask because the BACKLIGHT heat would have no effect on the fan that is mainly to exhaust the CPU/GPU heat.
So...
I'd concentrate on the following:
1) 1920x1080 just because:
https://www.laptopmag.com/articles/laptop-screen-resolution-ripoff
2) Quality/reliability matters the most too (try to find user reviews on places like NEWEGG... Amazon is no good since they mix similar items)
3) for CPU I recommend Intel that has 2C/4T (dual core with hyperthreading) not 2C/2T
4) if possible find a model that has an extra M.2 or SATA slot to add another drive (so you can backup data). It's hard to find out though what a model offers for this.