With eInk screens it's an interesting story. Because when your page is shown, there is no need for CPU at all for keeping it, so in an ideal world for such devices every page flip is a micro-cycle of waking up from the deep sleep, doing a job and going back to sleep. With such a lifecycle it's even better to measure the battery life not in hours but in page flips. When KOReader supports going to the deep sleep between flips then the difference between it and the bundled software should be small. But if for some reason there's no going to DS between flips, the battery life will drop significantly and back to time units per charge.
On my Paperwhite from 2018, the battery life is better on KOReader than on Amazon’s firmware.
What device? I haven’t noticed an issue on android devices. On my rooted kindle it is a bit less battery but I haven’t measured it.
On my Kobo Libra 2 I never noticed a difference.
I installed on a brand new kindle and didn't notice any difference.