Predator benefited more from AvP than Alien. The seven years between AR and AvP was tied for the longest gap in movies in that franchise, compared to 14 years for Predator. Alien had more solo games and merchandise as well.
None of this is to talk trash, it's just that Predator hit a wall as a franchise after Predator 2 which it has since recovered from. 3 of its 5 movies were made in the last 12 years.