I still have not seen The Predator. I will also admit I'm more of an Alien fan than a Predator fan. This does not mean i don't like the Predator movies though. In fact Predator 1 is a classic! Predator 2 was also pretty good. Predators was ok and I enjoyed it. Both AVP movies sucked, but the original comic was amazing.
That being said i really feel that Predator showcases the Alien waaaaay more than vice versa...in fact i don't think the Predator has been showcased in any stand alone Alien movie at all.
I think Predator deserves a true Predator fan to direct the next movie, and no Alien stuff!