The pyramid is an interesting concept but I would argue it's not that well realized. It's barely utilized in the script except to divide the characters. You'll note it's never really utilized in the main concept of the film. The Alien versus the Predator in a moving pyramid... Ya know?
Just imagine having the Celtic vs Grid fight broken up by the Pyramid shifting, and Celtic's arc became almost Ahab-esque where he's trying to find and kill Grid to avenge his fallen brother Gill.
As to AVP-R, it has plenty of interesting ideas, but it again, doesn't make the most of any of them. People keep saying Wolf is a great Predator, but he's really not. His opposition is
trash. It's one of the very few things the script actually did better than the final film, showing Wolf actually having to fight the aliens and taking injuries.
Remember that scene in AVP:R where the alien is eating the body, and Wolf just sneaks up behind it and stabs it with his spear?
This is how that was originally scripted:
Poor writing in the script aside, the concept was actually better before it got finised down into "Wolf is a badass. Wolf is a badass. Wolf is a badass."
You can't really have tension, excitement, etc... If the Predator just steam roles the aliens.
By that same token I think this will likely be a weakness of The Predator. The Upgrade will doubtless steam roll the others and that really makes me sad. It's a tired Hollywood cliche.