I don't think the Predator series has dropped the ball all that much. At least not with the first 2 films, perhaps slightly with the more recent Predators. Predator 2 changed the setting and increased the Predators arsenal of weapons. We also were treated to the interior of the ship and the introduction of their potentially clan based society. This is/was enough for me. And really Aliens didn't do too much more than that. Sure, there were a hell of a lot more of them but that's akin to the Predator's increased weaponry. The Queen was a big reveal, and does perhaps trump everything that Predator 2 had to offer, but it's not all that different from seeing the other members in Pussy Face's clan, even if Danny Glover didn't have to throw down with them.
I agree, Predators didn't do much. It introduced the Berserker and BSP and Falconer but didn't do enough with them to highlight their differences. And yes, setting it on a different planet didn't do much for a change of scenery. As is known though FOX wanted to take the audience back into the jungle, giving the audience what they know and love so to speak. The fact that Predators take humans, and other creatures, from Earth and elsewhere and bring them to game reserves is new though. Maybe not to the comics, or games, but for the movies. The Predator Dogs were a welcomed addition as well.
What did Alien 3 do? It took us back to 1 Alien. Sure, the twist was it burst forth from either a dog or oxen. Of course the primary focus of the films at that point was on Ripley and the company. A reoccurring main character and mysterious and often "evil" company is something that benefited the Alien films, and that the Predator films are lacking. I however don't see the need to a reoccurring main character. As i said, i view Dutch's and Harrigan's stories to be done. As for government involvement Predator 2 did introduce us to O.W.L.F.
Really there isn't that much difference in the amount of new components given to us by either franchise. At least that's how i see it. The key difference is the Alien films follow Ripley, whereas the Predator films only returning star is always the Predator itself. Each film has expanded upon the last, even if minimally. I myself am plenty fine with what we've been given and honestly don't need to be shown, in detail, every component of their society.