After the queen dies in the "Alien vs Predator" game, Specimen 6 becomes the new queen because she is the strongest living female left in the area, if I am correct. My question is: what if the only female left was a Predator-Xenomorph or an animal-Xenomorph, like in Alien3? Would it produce different facehuggers, or just manage to be even more frightening?
I think that non-human Xenomorph queens would be able to produce more dangerous offspring, especially in the case of a PredAlien.
I'm taking into account their more powerful nature. The hybrid from AVPR manged to wipe out a whole Predator hunting party, not to mention multiple humans before it got killed.
So I think the answer is yes, and they'd make even more deadly critters than human-based Xenomorph spawn.
Depending on the particular brand of canon you subscribe to, the Xenomorphs have absolutely zero bias towards reproducing using humans over other species, they're simply the most common prey of the right mass seen in the stories (other creatures used include Cows, Dogs, Yaut'ja and a hilariously wide menagerie in the comics)
So given that pure-strain Xenomorphs are not specifically born of humans, I'd say that there's no reason you couldn't get a Queen from another species.
I'd also expect that since the strains we see are all human-born, including their queen, we'd likely see a different variety of xenomorph queen into the bargain.
Based on one of the video games, Alien vs Predator: Extinction, in order to make a queen, a special face hugger is laid. That face hugger will make a pure-bred Praetorian regardless of what the host was. If the queen dies, one of the praetorians will take her place.
If this is canonical or just made sense for this game is up for debate.