Launching apps on my iPhone 6 (which needs a new battery) takes for ages (even when compared to my older but less used iPhone 5S). I can't imagine that the extended "screen lit"-time does not have a big impact as well.
Also: I am one of the few users who would be totally fine with the iPhone shutting down at 20% or so (if I have the full performance as I used to) because my iPhone is rarely going near 20%. At work I can charge. At home I can charge. When I am on the go I usually am not using the phone that much... However playing hearthstone when I am in bed, loading the phone, everything takes much longer as well which makes playing games less fun...