I know the plastic sheets stop drafts big time. Whenever the wind blows outside, the plastic on my windows bows into the room. If that kind of draft were blowing against draperies, they would just move and wouldn't keep the draft out.

I use both. I have a very large window in my bedroom. I have a plastic sheet over it, then heavy velvet draperies that go to the floor. I made window quilts (Roman shades made of cheap pre-made quilts from Walmart) that fit inside the window frames in the living and dining rooms. They insulate quite well and I get lots of compliments on them. Instructions are free on the internet if you Google roman shades. They only cost me about $30 per window and I couldn't buy good quality draperies for that.

If no study has been done on the effectiveness of plastic sheeting to keep heat, then there should be no claim that drapes are better or worse than them. The article reveals a bias, not science. (We'll forget the fabric pun of "bias"...)