For Alien, it's all about the horror and style. The sexual horror, specifically. And not showing the monster all the time. That and the world building. There was such wild intricacy in the first film. It was so crazy, yet still felt so plausible. The sets are also a big part of it. The Medbay on the Nostromo, the Derelict, the colony of Hadley's Hope, Fury 161, even the company. It's as if the sets are a character in their own right. The environments for these movies have been spectacular. I can't lie, it's all of it really.
For Predator, it's the one-sidedness of the fight. The idea that even experienced soldiers can be outfoxed and out-maneuvered by this creature. But mostly, for me, it's the idea that there is something out there in the dark that's actively hunting you and enjoys what it's doing. You have a hard time seeing it when it's right in front of you. It could be above you, behind you, and you'd never know it. As humans, we're used to doing the hunting, the consuming, ect. The mere idea of being hunted or eaten by anything is horrifying to us. Predator turns us into game, the object of sport, putting us constantly on the defensive, and that's scary.