Well, I can at least try to explain why Alien 3 is the closest one to my favorite, if someone would put a gun against my head and force me to chose one from the trilogy , which I consider as one and love equally. But Alien 3 has that eerie feel that I never found in any other movie. The way it opens, the chilly soundtrack, the dirty, basement like environment, the loneliness, the helplessness, the gruesome alien (its birth especially) lurking somewhere, the drama of Ripleys character with "terminal illness", theres so much richness to it, and the moody feel is really unique
Perhaps Nostalgia also plays a factor, since it was the first Alien movie I saw when it first got released on VHS and the movie that got into it all