An AVP stand-alone, not directly in either universe a sort of Blade-Runner city on a moon of Venus say, Predator is doing his usually business as a militant government take over, people aren't happy. Riots etc
And in all the chaos only a few people realise others are going missing, but the good cop investigating it thinks it's the government kidnapping people as the Predator hunts down this new government force ( They have new tech, prototype military powerloaders etc
The cop also does his investigating and calls in a few favors from friends in the government, but what they don't know is the reason the government quarantined an isolated part of town, they found an Alien and it's getting out of hand, (They were doing construction and broke into a giger-esque cave beneath. This could show some of the more predator aspects of the Xenomorph hunting down marines. (Government marines.
The unique thing about the film would that it would have it's own political commentary, characters with genuine depth (Spend most of your time with one character and four at the most well developed other characters.
Some marines, some government guys and some just people each with their own perspective on the militant take-over. But with their own theory as to why people go missing.
Also their would only be one alien and one Predator. Each taking fodder(but politically important fodder, marines go missing because of the alien no-one knows about and the predator works his way up the political food chain.
(This is also a reboot just titled: Alien Versus Predator)
Egg morphed people are found at the end of the film if you're wondering.
And also the Alien is different, more giger than ever having gestated in an Android.
You could have the mystery essentially be the meat of the film and also, the Predator and Alien fight twice, once in the middle and the Predator is dealt a severe injury and is out of the game temporarily. This is after the reveal that one of our main character's friends has been feeding information to the government about their investigation.
I envision the fights to be slow paced, rather than action-packed.
They nearly gut their lying friend but she just thought she was doing the right thing.
I think the film would end with similtanously with our investigator's being revealed as Weyland spies, the informant to the established government runs in fear. Whilist the person "good cop" we thought we'd be rooting for hunts her and is promptly ambushed by healed Predator (Predators re-entrance) and the predator promptly guts him violent and takes his skull and spine.
Our new female protagionist leaves the planet immediately fearing for her life as the Predator comes close to killing the Alien and he does but the Alien then explodes! (A trait of being android produced) The chap showers the Predator with blood on a rooftop.
I'm not sure if the Predator should activate his bomb or not at the end, if Weyland then comes in and retrieves the eggs held in the abandoned part of town where he alien took it's victims.
Sorry this first draft is very rough but it's what I'd like to see.
Then you can up the stakes in the sequel and call it Aliens Versus Predators. (Not related to the Predators movie, just like the sound of the title.) And even harken back to the original comic books by calling the third Aliens Versus Predator, Font and all.