The first AvP was an incredibly scary game, and really captured the atmosphere and tension of the Alien movies. After a while, the beeping of the motion sensor was enough to shit your pants, which is why they packaged the game with a free pair of underwear. However, it was also incredibly hard and featured no real mid-mission save system until the Gold Edition. Even the acid blood, which sprayed for what seemed like tens of feet, could end your life if you weren't careful. The aliens respawned periodically throughout the map, so you were never safe. There also wasn't any real story. Or, there was a story, in the same way that early id games had stories. Which is to say, there wasn't any real story.
AvP 2 was kind of the opposite, in that it had a really solid story, with good narration during cutscenes. There were strong characters that you grew to recognize and connect with. However, the fear factor kinda left the game, because I didn't really feel scared at all while playing through the Marine campaign. The aliens seemed much less threatening and deadly, and their acid blood was basically a nonfactor this time around. The game's lighting with the new Lithtech engine seemed a lot brighter, which probably contributed to this. AvP 2 is probably the better overall game, judged by today's standards, but it definitely lost a lot of the intensity that made AvP so memorable.
If you're looking to get scared shitless, then play the first PC one. It's by far the scariest. If you're into a more well-rounded experience, then get AvP 2.