How did a franchise with this potential end up with us ever doubting the power of an Eldritch Abomination beyond human comprehension?
The argument should not be:
"Would an Alien or a Predator win?"
It should be:
"What tactics can a Predator use to defeat an Alien?"
Why?
Because the franchise itself implies it but fails to capitalise on the potential for truly impressive battles. Aliens may be the whipping boys in terms of the output material, but Predators are equally as let-down. Instead of being clever and resourceful, they're limited to be being humanised, bronze-age hero archetypes. Anderson had his faults but he got this right. Celtic is set up to defeat Grid, not due to his own strength, but due to his quick-thinking. In an instant, he thinks of using his netgun to trap Grid and it's only his arrogance afterwards that lets him down. That was tense, entertaining and a testament to the combat adaptability of both species.
The entire underlying concept of an Alien is its superiority. Its structural perfection is matched only by its hostility, and it's up to the Predators to overcome that. We rarely see that - we generally just see PUNCHURGHDEAD or BLAMBLAMBLAM. We don't see Aliens and Predators testing one-another's agility, cleverness, resourcefulness or creativity - at least, not often enough.
After all, Predators are elite hunters. Aliens are (probably) war-machines created via biotechnology for a lost but vastly superior race. Predators shouldn't want to have a stand-up fight with Aliens, because that's where Aliens are supposed to win via concept. Predators should win by using their hunting techniques, with emphasis on skill and judgement, not brute strength.