Here's my view:
The Preds of the the first two movies are more experienced than those found in AvP (with Pred 1 having the edge over Pred2). These Pred ventured solo into their hunting grounds with no backup to hunt the ultimate prey, humans (my opinion, not sure what the majority view is on this board). In AvP, if we forget that the entire point of any Preds going into the temple is to be "blooded" thereby making them younger, the Preds enter in a pack of three with a lot of equipment + the shoulder cannons they were suppose to get.
There's also the difference in hunting style. Pred 1 & 2, especially Pred 1, hunted smart while the AvP Preds just kinda ran at stuff.