In a fair one-on-one fight between Alien vs. Predator's Xenomorph and Predator aliens, it is difficult to know who would actually win. However, the outcome of such a fight would depend a great deal on the rules of said fight. In Alien vs. Predator, there were many fight scenes between the Xenomorphs and the Predators, but none of them were technically fair, because each species always made use of their distinct tactical advantages. For the Xenomorphs, that advantage was stealth, speed, and the element of surprise. The Predators' advantage was their use of advanced technology, and the support of their advanced civilization. Therefore, none of the fights in the original crossover movie made it clear who would win in a fair fight. Additionally, the original movie's final Predator was only able to defeat the Xenomorph Queen with the help of human scientist turned warrior Lex (Sanaa Lathan).
Likewise, in Alien vs. Predator: Requiem, the many altercations between the species didn't clear up who would win in a fair fight either. Even the final hand-to-hand battle between the Predalien and the movie's final Predator ended in a draw. Additionally, the invasion of Xenomorphs in the movie was not actually stopped by the Predators, but rather by a human military strike which eradicated not only the Xenomorphs, but the entire town as well. In both movies, the Predator species was only able to overcome the looming threat of the Xenomorphs by using some combination of advanced technology, alliances with humans, or support from their own advanced civilization.
As such, none of the fights between the Xenomorphs and the Predators can realistically be classified as fair fights. The rules of a fair fight would presumably remove all unnatural advantages of both species. In general, that is stealth for the Xenomorphs, and technology for the Predators. Any one-on-one fight where a Predator alien was allowed to use its advanced technology against the Xenomorph would clearly favor the Predator. Likewise, any fight where the Xenomorph was able to use its stealth abilities would clearly favor the Xenomorph. Therefore, the only way to know which species would win in a fair fight would be to pit them against each other in something akin to the roman gladiator games—a no-holds-barred fight to the death in a well-lit, open arena from which escape is not possible.
This is the only situation in which a clear winner in a fight between the species could be determined. The outcome of the fight would be the result of each species' natural strengths and weaknesses. Both species have immense strength, agility, and ample fight IQ; however, the Xenomorph clearly has natural physical advantages over the Predator—namely its long, blade-tipped tail, its inner jaw, and its acid blood. It also has the ability to fight from either a bipedal or quadrupedal stance. Based on this gladiatorial combat scenario and each species' natural abilities, it is quite clear that the Xenomorph would be the winner in a fair Alien vs. Predator fight to the death.