I doubt it has much to do with the base material. 120 and sheet film is coated on both sides with gelatin. One side obviously for image-making, and the other side to counter the curl that you'd inevitably get if you were to coat only one side. So "counter-curl", in a way. The interactions between these coatings would affect reel-loading characteristics as well as curl characteristics. Much more so than the actual base material that's inside the sandwich.
Having said that, some materials have a better mechanical memory than others. Roll film is (surprise surprise) rolled up, so the film tends to 'remember' the curl.