Yep, you can play them on the PS 2. I would get them both if you can; both of them have something different to offer. DC 1 is a scary game- it's much like the first few Resident Evils in being survival horror. DC 2 plays much more like an action game.
Personally, my fav is the first. It's got a really good storyline, and quite a few moments where you'll jump. However, that said- there's about fifty or so dinosaurs to kill in the whole game and not a whole lot of ammo, so if you're looking for action DC 2 is the way to go.