I've got a modern CIII bag and an original(ish) CIII bag, and the difference in thickness is pretty obvious, the modern one is the same material as they used on the Heritage to G4 bags originally (after that they used the inner lining material for replacement bags for the CIII and Tradition), but the original one is like it's made from a wool blanket, and is heavy...
Still, modern shakeout bags are made from better materials, which are able to filter better and hold more dirt in, though you shouldn't use them if you or anyone in your family suffers with breathing problems, I don't, but I always sneeze when using my Kirbys with their shakeout bags... :S