The Alien vs. Predator franchise really is a match made in heaven.
Aside from the serendipity of both franchises being owned by 20th Century Fox, and both having their comics licenses extended to Dark Horse Comics who first came up with the idea, there's a lot about the franchises themselves that make them perfect for each other.
To start with the obvious, the Predators live to prove themselves by hunting the deadliest and most fearsome species space has to offer, so what better to pit themselves against than the most terrifying science-fiction monsters ever conceived? The Alien makes for exactly the kind of thing you can believe would be a credible threat to a Predator, even with all of his advanced technology, able to turn the tables and hunt the Predator back — and perhaps come out the winner.
On that level, the Alien is a "hard-counter" to the Predator. The Alien has no eyes or other obvious sensory organs, yet clearly has extraordinarily keen senses to home in on its prey. One of the Predator's most iconic and useful tools is its camouflage system, rendering it all but invisible... but what does invisibility mean to a creature with no eyes? In Aliens, the marines use infra-red sights to try and see the Aliens about to attack them in the hive. Dietrich says "Maybe they don't show up on infrared at all," right before getting grabbed by an Alien she'd been looking right at as she spoke that line, indicating her speculation is entirely correct. Predators naturally see in infrared, meaning the Alien is normally completely invisible. When a Predator stalks a human, its IR vision and cloaking means the human can't see the Predator, but the Predator can see the human (almost) no matter how they try to hide. When an Alien stalks a Predator, the Predator can't see it, but it can "see" the Predator no matter how he tries to hide.
But more than that, the franchises themselves are kind of perfect yin-yang.
The Alien franchise is well-regarded as a landmark in female representation in cinema, with all the films revolving around a female protagonist, and Aliens having as it's climax two Mama Bears fighting over the fate of a third female child. And the design of the Alien itself, while unsettling and terrifying, is also beautiful, with HR Giger having notable sexual elements in his work that the Alien embraces fully.
If one wants to expand that train of thought, then the Alien represents fear of sexuality, perhaps specifically male fear of female power. Dan O'Bannon was quite adamant that the facehugger victim in the first film be male, feeling a male audience would be titillated instead of terrified by a female character in the same situation. If that's the case, then the strong female protagonist of an Alien film represents the acceptance of feminine power as not only not a threat, but a potential savior of mankind.
Compare Predator, the manliest movie ever made, featuring big icons of 80s masculinity being stalked and murdered by an alien who is, in pretty much every way, an exaggerated male. The Predator himself is manly, engaged in a masculine activity to boost his male ego. The film Predators run the gamut from noble and honorable warriors to asshole Blood Knights to insane Egomaniac Hunters, reflecting a certain sampling of cultural views on manliness.
Thus does Alien vs Predator strike that yin-yang balance, the hypermasculine Predator versus the not-really-feminine Alien. And this really shines in the original Alien vs. Predator comic book.
There, we have several examples of Predators, from the noble and honorable Broken Tusk to the indiscriminately violent others. Looking back on it today, the young, angry Predators come off as an embodiment of toxic masculinity, hunting and killing just because they enjoy it instead of with rules for a purpose (esoteric though the purpose might be), while Broken Tusk is a more positive male example, defending those who should not be prey and taking his wayward hunters to school as he encounters them. But what really seals the deal here is the main character of this comic, Machiko Noguchi.
A strong female protagonist very much in the Alien franchise mold, she and Broken Tusk team up to end the Alien threat and save the lives of the colonists. Where the yin and yang are at war in Predators vs Aliens, they are in harmony in Broken Tusk and Machiko. Only together can they triumph.
This is the lightning-in-a-bottle that the original comic captured, but has never quite been duplicated since. While it's quite easy to enjoy the franchise on the level of Aliens and Predators kicking the crap out of each other, each franchise has its own deeper meanings, which branch out into other deeper meanings when they are combined. Two disparate things, coming together to create something else new, and different, and wonderful.
Yin and Yang.
