Should they make a new AVP movie on one of the home planets?

No as it would be too one sided for whatever species planet the movie took place on. With empresses queens, and a queen mother running around predators would not be in for a good time, and with all the best predators with all the gear they could ever need aliens would get slaughtered

I think they should because I love AVP 3

Yes it is true either side would have a home field advantage but does Alien have an actual "home Planet" but what if they made a movie that showed how the predators first discovered the aliens that would make a good movie and one i would want to see.

  I agree with E123 omega>     that would tie some things together.

It's cool but it gives a home advantage so the other side would need a "boost" of some kind to be able to even things out.

yes i would like it. the pedatore ans alien homeworlds

I definitely say they should! That would be awesome. 

They should set it on one of the home planets, or at least in the future and in space. The home planets have already been heavily hinted at, check out the speculation about the possible sequel:
Alien vs Predator 3