Plastic bags take up less space in a landfill than paper bags?

I do not exactly know how plastic and paper bags are taken up space in a landfill. Given my consumption pattern, I expect that plastic bags are taken up more space in a landfill than paper bags. I visit convenience stores a lot. Whenever I go to the convenience store, employees provide plastic bags to pack stuff that I want to buy. Because of cool beverages and refrigerated foods, they give plastic bags rather than weak paper bags. According to BBC news, paper bags are greener and more eco-friendly than plastic bags. I want to say to customers that totally not using planting bags is impossible, however, we should try to reduce the amount of consumption of plastic bags.