A well-armed Pred with decent hunting experience should have a major advantage over an Alien.
It helps tremendously that they have technology, including a vision mode which highlights an Alien's entire body in glowing green. This doesn't get emphasised enough I think.
Adolescent Celtic was missing a shoulder cannon and acid-resistant gear. Being inexperienced, he took his time trying to savour the kill when he should've hurried to finish his foe before the net dissolved.
The Alien is the superior natural weapon by far. With the right equipment, odds swing back heavily in favour of the Predator. A highly claustrophobic environment, more navigable by the Alien than the Pred and limiting the Pred's range, evens it out.