What I do love about Alien 3 is that it's the first (and last) character movie of the franchise. This doesn't just come through the prisoners and their keepers, but through Ripley as well. For the first time, she's an inherently interesting character in her own right, with or without an Alien or twenty threatening her. Where the first film was a haunted house movie in space and the second was an optimistic Reagan-era military thriller, Alien 3 is first and foremost about people and about the redemption of those many of us dismiss off hand. Turning murderers and rapists into sympathetic characters isn't easy, but Alien 3 pulls it off.
Another thing I really enjoy is the Alien as something implicitly supernatural or paranormal, or at least as a creature experienced as supernatural. The first film was rife with this, through the Jockey ship to the bizarreness of the creature itself, but the second film brought a hive-like structure and a firmer biology to the creature that demystified it to some degree. In turn, this paved the way for a lot of awful expanded universe media that is only somewhat redeemed by the Alien vs. Predator games. But Alien 3 knows what horror is and I fully support the notion that the Alien always wins. Throughout the arc of films one to three, Ripley's victories are Pyrrhic at best. After all, this is not an American horror franchise as such, but the brainchild of Dan O'Bannon, Ridley Scott and H.R. Giger, and there is no cultural requirement that the good guys truly "win" -- unlike many purely American horror franchises and films.
So I appreciate Alien 3 for being true to the potential of the Alien as a monster, but also its attention to characterisation. It's not a movie in which a lot really happens, as such, but there's a lot of character interplay that lifts the potential of the series, and it does that without losing sight of the horror of the Alien itself. And most of all, it leaves much of the details of the Alien up to interpretation apart from its strength at environmental adaption. It's not clear how conscious the Alien is of its actions, nor are its intellectual or physical limitations made perfectly clear. A monster without mystery is no monster at all, and that's what a lot of Alien-related stuff has forgotten since Alien 3.