The Youngs Modulus of a material is an indication of that materials stiffness. The Specific-modulus of a material is the Youngs modulus divided by the density. Isotropic materials have similar stiffness, strength etc in all directions (up down left right; 3 dimentionally). Steel is generally isotropic, CFRP is anisotropic.
Most structural materials (steel, aluminium, titanium) by an odd coincidence have roughly the same specific-modulus. However CFRP has a much greater specific-modulus than steel, it can vary but is very roughly 3 or 4 times greater. So comparing a set of steel forks with a set of CFRP forks of the same weight; the CFRP forks could be 3 or 4 times stiffer. But since CFRP is not isotropic this will not always be the case.
Carbon Fibre is string, and CFRP plastic is plastic with string reinforcement. So it depends very much of the type of plastic that the carbon fibre is reinforcing. Particularly when the CFRP is in compression; string is good for pulling (tension) not so good for pushing (compression.
http://www.aluminium.matter.org.uk/content/html/eng/default.asp?catid=89&pageid=2144417038