The Alien campaign is, unfortunately enough, the weakest part of the play experience. I mean, don't get me wrong, the first level with the whole life-cycle and the escape from the compound is pretty cool, and works well, but that's all there really is to that third of the game other than picking up more of the over-arching story. Good wall-walking though, best I've ever come across anyway.
The Predator campaign is pretty fun in a Thief kind of way, actually, or at least I always thought so. You've got a pretty powerful bag of tricks at your disposal, but ultimately you're not very strong and you've got to learn to your tools together in an effective way to keep yourself going. You CAN try to just blow through the Predator levels as an unstoppable juggernaut, but you'll probably die a lot. In a way, the devs captured the Predator's habits from the films very well...it just makes for a somewhat obtuse game experience. Also, collecting skulls is fun no matter what. I love the Predator's laugh when he decapitates someone, it sounds like he's having such a great time.
I'm also gonna echo that the Marine campaign is the best part of the game. For atmosphere, tension, frantic action...they perfectly, perfectly captured the feel of Aliens. When I'm playing as a Marine, the game works at my nerves in a way that only System Shock 2 has otherwise. It is fairly linear, but it's a great play experience that hits all of the major points you would want out of an Alien franchise fps, and manages to tell a pretty good story too.
A flawed game, and perhaps overrated, but also a really good experience well worth your money. If they had made the damn AvP films like this then they would have been pretty great. Alas, alas...