This is by no means well-thought out or with any solid arguments, and probably will have to be revisited once I’ve done further research, but I needed to get this on paper.
Alien feels like a very feminine franchise whereas Predator feels very masculine, in the traditional sense of both words. Please keep in mind that when I speak of masculinity and femininity in these films, it’s in a very traditional (sometimes veering into stereotypical) sense.
Also keep in mind that the only Predator movies I have seen are Alien vs. Predator and Alien vs. Predator: Requiem, and I freely acknowledge that the latter likely adds no more to the Predator franchise than it did to the Alien franchise, which is zero. I will not be counting Requiem as part of either franchise for the rest of this post.
So going off of the enjoyable AVP film, this is where the contrast was immediately highlighted for me. For one, the Alien films all have a female lead, even Prometheus: Woods, Shaw, and of course Ripley. With the exception of AVP, all the Predator films have male leads (or so IMDB tells me. Weaver did get second billing when the first Alien film came out. Maybe Predators did the same?).
The design of the monsters in the AVP film also seem to have distinctly feminine and masculine features. We hear of the square jaws of heroic men and the curves of beautiful women. The Predators have a very geometric aesthetic, the xenomorphs are all curves and fluidity.
The actions and very presence of the two aliens are also in this dichotomy. The Predators take up space; they make their presence known. Their threat revolves around technology and the destruction of life (men are stereotypically the ‘violent’ sex). The xenomorphs flit from shadow to shadow; they make themselves small. Their threat revolves around reproduction and the birth of new life (women are traditionally the nurturers).
I definitely want to revisit this hypothesis after I watch the Predator films.