Well, what was wrong with the waxed cartons?
Waxed cartons are fine; they do cost a bit more than plastic as I remember being taught (I’m in medical not food packaging).
Most of the cartons I have seen today are hot form/fill/seal single serving. That’s the kids’ juice and milk cartons you find unrefrigerated.
Larger containers (gallon jugs) are blow molded usually from polypropylene. They’re very thin and use little material. That’s why they’re used now (but you can’t hot fill for sterility).