I don't know what accounts for the popularity of monkey movies. Not just the multiple incarnations of Planet of the Apes, but there's also King Kong, and … well, here's a list. Go for it.
That being said, I'm a fan myself. And this one is pretty good. You'll want to have seen the first two in this series first, though.
As the title implies, it's apes vs. humans, and there's no doubt about which side we're cheering for. All the apes want to do, pretty much, is live peacefully in the forest; but the humans, for some reason, are trying to wipe them out. (Speaking of monkey movies: one of the attacking army has "Bedtime for Bonzo" scrawled on his helmet. Heh.)
The humans, at least the ones surviving the "simian flu" outbreak described in the previous movies, are still technologically superior. And it doesn't help that some of the apes are dumb enough to sell out their side. The human leader, Woody Harrelson, is ruthless and demented. And he goes too far in one of the attacks, causing the normally-peaceful ape leader, Caesar, to embark on a path of revenge.
Film buffs will recognize a lot of inspiration from non-ape movies. Comic relief is provided by "Bad Ape", played by everyone's favorite goof-actor, Steve Zahn.
Purists might gripe at the massive deus ex machina at the film's climax. I was about to, but… hey, it's a monkey movie. Slack is demanded.