I actually rewatched the film recently and I think I really, really like this film more now than I have had for years before. For the record, I watched it as a youngster and loved it, but seeing it in context as a grown-up kind of altered my vision of it. As part of either series, or as a link to both, it doesn't work for one simple reason -- as a concept, the "VS" idea is far more pulp than either Alien or Predator because it's done for the sake of pitting two popular film characters against each other.
So the movie, being an adaptation of the comic, starts with the "wrong" route and cannot steer in a "right" direction that surely and inequivocably fits both series, also because they have 'tonal rules' that are difficult to conciliate into a single narrative. For example, by making the Alien the prey of the Predator and thus having the human characters just caught in the crossfire robs the film of the 'being hunted' aspect of the Predator films (which is their entire point).
But what did the movie want to do? It wanted to adapt the comic -- and that's what it should be seen as: a comic book movie that channels the two iconic characters into its own version by the way the comic book portrayed them. Aliens and Predators become stylized characters: big talons for the Aliens; big blades, big guns, more muscles for the Predators. They're not the original creatures, they're how a comic book "mind" would see them: exaggerated, pulpified.
The film acquires newfound quality and is much more enjoyable when the intentions at its roots are considered and it is seen as an echoing homage rather than an actual part of the continuity of both series. AvP is a creature-feature-based comic book movie.
There are many great aspects to it: the story moves at lightning pace scene after scene; the photography (composition, colours, etc) and visual storytelling of it are nothing short of excellent; the special effects are top notch and to this day represent one of the industry's finest combinations of practical and digital effects; the score is also serviceable and memorable enough.
With that said, of course there are flaws to be found and those are mostly within the script. Cringeworthy lines like "my experts tell me... it's a pyramid" and underdeveloped human characters seem to suggest an unfinished script, a draft that absolutely needed a couple or more passes before being subjected to production. The team-up also represents a jarring tonal shift within the narrative (the 'running together in slow-motion' shots are downright embarrassing).
Personally, the good parts ultimately outweigh the bad parts, and I really enjoy the film for what it has to offer. It's a fun ride.
