I think it depends on the user too. SpookDroid notices the difference. I can't see any difference on a 55" LCD TV screen at normal viewing distance between HD video and 4k video unless I get close enough to see individual pixels - and with plastic implants in my eyes, II have near-perfect vision. There's nothing I can't read on my Note 3 - maybe if someone comes out with an app with a 1 pt. font I'll have a problem, but that's difficult on paper too.
As for the battery, it also depends on the screen technology. An Amoled screen's power drain is mostly influenced by color - if it's displaying black, even an 8k screen will be drawing nothing. But if it's all white, a 4k screen with more pixels will be drawing a LOT more current than an HD screen. Straight LED screens will draw a little more for more pixels, but not enough to save more than a few minutes of battery by making it a 1080 screen.
The big advance is going to be in batteries. Once the automotive industry solves their problem (you don't see many cars with lithium batteries - they fail too often and are too expensive to replace), the cellphone battery industry can use the same chemistry or physics (whatever is developed) to give us 10,000 mAh batteries in the same size as the current 3,000 mAh ones, and for not much more money. Then we'll stop worrying about another 10 minutes of SoT.