The Xenomorphs of the Alien franchise and the Predator race have fought many times across different forms of media, most famously in the equally loved and derided Alien vs Predator, but their original clash happened in Dark Horse Comics' Aliens vs Predator. Differing from the eventual film in some key ways, this original clash had a definitive victor that may surprise some fans.
The Xenomorph first appeared in 1979’s Alien, directed by Ridley Scott, while the Predator first appeared in John McTiernan's Predator, from 1987. Both franchises were owned (at the time) by 20th Century Fox, thus creating the possibility for a crossover. Sure enough, the original Aliens vs Predator story appeared in 1989 and became a smash hit, published in Dark Horse Presents. Told over three issues - only the third of which brought the properties together - this short story was then used as a prequel chapter (or issue 0) to the five-issue Aliens vs. Predator limited series which truly saw the two monstrous extraterrestrial races come to blows. Many more Aliens vs Predator books appeared over the years, all published by Dark Horse Comics. The idea proved irresistible to Hollywood as well: a Xenomorph skull was briefly seen in Predator 2 and in 2004, after years of development, the first Alien vs Predator film appeared. It was not a critical hit but did well enough to justify a sequel, becoming a cult favorite to many fans.
The story begins with a Predator ship distributing Xenomorph eggs on a distant world; their plan is to let the Xenomorphs reach maturity and then return to hunt them for sport. While a Predator known as Top-Knot carries out a Xenomorph hunt elsewhere (scoring the alien race's first victory against their Alien opponents), another party arrive on a seeded planet to start the hunt, but there is one factor they forgot to take into consideration: humans. When the Predators last scouted the planet, humans were not living there, adding a wildcard element to the Xenomorph/Predator clash. The human presence allows the Xenomorph risk to quickly grow out of control, but ultimately also provides the tools and assistance for the fight to end in favor of the Predator.
How did humans change it up? The humans had the technology to kill the Xenomorphs, but they had no defenses against the Predators. There are numerous scenes in the first miniseries of humans killing Xenomorphs (though there are plenty of successful chestbursters as well), but no comparable success against Predators. The humans do manage to take a Predator captive, however, and this captive, named Broken Tusk, ultimately helps the humans, turning on its people when it realizes that innocent deaths are on their hands. The Xenomorphs put on an impressive show, but between the Predators and humans, they're defeated thanks to the sacrifice of the human colony of Prosperity Wells.
An entire colony of Xenomorphs, including an Alien Queen, are able to take residence on the spaceship Lector due to human error, but are ultimately wiped out by a human named Machiko Moguchi and her Predator ally, who brands her as a fellow hunter before dying from its injuries. The surviving human colonists are granted safe passage to another planet, but Machiko stays behind, waiting for the Predators to return for the planet's next seeding, and ready for some vengeful hunting of her own.
Throughout the comic, the Aliens are treated as a ravening horde, with individual Predators more than a match for the Xenomorphs one-on-one. While the comic's Predator hero does perish at the end of the story, it's only after achieving the larger goal of wiping out the Xenomorphs and sparing those humans who should never have been put in harm's way, with Machiko explicitly carrying on her ally's legacy. Elements of this story would appear in the later Alien vs Predator movie, but in the very first Dark Horse Comics story, it is made clear that the Predators are the obvious victors when the two species clash, and the Predator-human alliance is able to fend off the Xenomorph infestation, albeit with heavy casualties.