Original ending had the apes offing everyone in Caesar's city. In light of Watts riots and others, film was recut with Roddy McDowall dubbing a speech for compassion. ("We who are not human, can be humane.") You can kind of hear the timbre change - he is not speaking through makeup. (funny enough, another anecdote from 'Escape from the Planet of the Apes' - McDowall and Hunter were overdubbing and couldn't get it to sound right until they put on the mouth prosthetics!)
And, it took me years to figure this out - it's not necessarily that the apes win all over. But, they destabilize the world enough that mankind starts shooting off nukes - either to suppress the apes or to take advantage of their enemies during the ape riots. Some apes flee the cities before the bombing starts.
It is funny now listening to that speech knowing all the background info, and it does sound like Roddy was in a hall way or something, just a total different sound and all the cuts to his zoomed in eyes.
Had they stopped with Conquest, it's a pretty simple "Apes win, man are slaves". When you throw Battle into the picture, it definitely lends itself more to an evolution (though not the way Col. Taylor thought). The TV series wouldn't have made sense without Battle (it DOES have umpteen chronological problems on its own).