B&W Rohacell vs woven Kevlar

I doubt that the material the speaker is made of makes a difference. A stiffer cone would cause a more piston-like movement with perhaps less cone breakup, however, I would think the driver's cone material, magnet, spider, magnetic gap, crossover, cabinet, and many other parameters, all contribute to its total performance.

correction: paper Kevlar instead of woven Kevlar.

Actually I am comparing 800 series vs CM series. I am not a big time classical music listener. I listen to 1/4 classical, 1/4 jazz, 1/4 house & 1/4 everything EXCEPT rap or most country musics. I am wondering maybe 800 series is more toward classical and CM is more to AV or pop music, therefore I am trying to find out the effects of these materials... Any suggestions?

The material is important as you want the cone to be fairly stiff but also to be internally damped. Stiff and light is good but you don't want the thing to ring like a bell. So a weave or a pulp construction or a light fabric impregnated with viscous damping fluid or two light materials sandwiched between a viscous fluid is critical to avoiding ringing.

B&W are often dismissed by audiophiles but in all honesty although they make more models than Imelda Marcius has shoes, they do use good materials for their midrange cones rather than cheap north european metal or ceramic drivers that ring like a bell (sound awful or need notch filters to sound mediocre)

Which is better for you ? I can't begin to guess - try to get some auditions in.