Turns out I never saw 'Battle for the Planet of the Apes', the fifth installment in the original series. How could I have missed it ?!
Thanks for correcting me, now I know what to look for
The most powerful scene, next to the ending of the first original movie which would be stupid to reveal for those who haven't seen it yet, is the scene (in the 2nd movie, I think) where surviving humans living underground worship a nuke in some kind of religious service. As a child that really left an impression on me.