In front of me right now I have an aluminium, ABS (plastic), Nomex and a paper coned driver and I am very gently tapping the cones with a pencil, just letting the pencil bounce under its own weight while holding it at the other end. I can easily hear a metallic ring (sound), a palstic sound (like tapping a plastic drink bottle) and a fairly neutral sound of both the Nomex and paper coned drivers.
Once you identify the particular sounds the different materals make you can from the back of a listening room identify the material a driver is made from. Personally I don't like music with a metallic or plastic bloom to it. No matter what crossover is employed you can't eliminate the inherent sound of the material. Where as "natural fibres" (Nomex is made from hemp fibres and can be bonded with a variety resins depending on the end use) including paper don't add much if anything to the "sound". But to make paper reatively stiff and hard wearing a variety of resins are used to achieve the desired result sometimes at the expense of weight. Very generally metal cones are lighter than resin saturated ones as there is less energy required to to move the cone, ideally as fast as the strings or reed of an instrument move, there by replicating the origional note in all its glory. But as said before, IMHO there is a down side to plastic and metal coned drivers.
Once you hear the sounds of the materials used in a drivers cone you will know exactly what I mean. Hearing is believing!
Cheers,
Laurie