Its half-truth. I agree that the initial Lollipop release ruined the battery timings, but later releases were perfectly fine, provided that the phone was factory resetted before and after lollipop update, wiped cache partition and ALL bloatware was disabled.
I myself updated about 25+ S4s (I9500, I9505, I337m) this way with very few complaints. They easily give 4+ hours screen on time with ~16-24 hours of charge on Lollipop.
Amoled displays fact.
Lollipop and Samsung TouchWiz UI is missing a basic principle that Amoled displays draw zero watt power while displaying full solid black backgrounds and least/minimal power consumption on darker backgrounds. Lollipop TouchWiz UI has white (light) backgrounds in most menus, messaging, stock wallpapers, dialers, etc which significantly increases power consumption in phones with Amoled display.
White or black backgrounds do not affect IPS displays power consumption much, but they do affect significantly in Amoled displays. That's why its recommended for Amoled displays to use darkers wallpapers, dark themes, dark backgrounds wherever possible, e.g Tapatalk dark theme etc.
Kitkat and Jellybean (dark coloured) TouchWiz UI was very brilliantly optimised for Amoled displays.
