I'm not saying that Danny Elfman copied Zimmer, because it's fairly short and easy cue, but still the indentical similarity is ovious. In Zimmer's score of The Peacemaker, there is that brass wich is pretty much the same that is used in the theme of Planet of the Apes.
Track 04: The Chase (in about 6:00 minutes)
Personally I think it's just a coincidence. Nothing more.