I've always assumed the change in predators face and mouth design came from Paul W.S Anderson's idea of humanising scar making his chin bigger and moving out the mandibles and for some reason maybe they the highest budget for making the animatronic skeleton and they just kept making new molds skins to put on top of scar predators animatronics over the years.
The flappy skin might be because of the latex getting soft, maybe stan Winston used a different type of latex on classic predator. Might be materials which today are no longer produced also because of environmental reasons, or they just shot the scenes for the original 1987 predator with the face fresh baked from the oven. My opinion is they should use some totally different material on the skin that connects the upper and lover mandible like rubber so it can expand and retract naturally and use latex for the rest of the face somehow.