Alex Mercer's bioweapon status is a diluted derivation of the elements that make him as he is.
In other words, he's not the 'pure' bioweapon the Alien is. He's signficantly more human and more vulnerable. Sure he can run ridiculously fast and overturn cars, but if the Hunters (if I remember their name correctly) can kill him, then so can Aliens.
And if the Predator is a match for the Alien, then the Predator can take him, too. Don't underestimate the ridiculous shit we've seen both monsters do.