I have experience in the development and building of Carbon Barrels and Carbon stocks with a couple of very well known companies.
PRO: Carbon is ounce for ounce 3 to 4 times stronger than steel - the ultimate tensile strength of steel ranges from 400 to 690 MPa, while the ultimate strength of carbon fiber reinforced polymer composites ranges from 1,200 to 2,410 MPa. It is generally 15-20 times stronger than fiberglass. Don't even ask how much stronger it is than any wood or other stock product, except maybe titanium.
PRO: Carbon can be stronger than Titanium or other matrix ounce for ounce but it would take some work to get it there. But then costs go astronomically higher.
PRO: I helped a company build a prototype Carbon Stock that was fairly basic through the build. We sourced 9k carbon, which is better than most other companies use with a strength of 7,523 ft/lbs, 396 g/m2. and built a standard sporter stock.
PRO: We slammed it on the ground, smashed it with a hammer, and then ran over it with a F250 in the parking lot. Wish I had photos of the faces of the folks there, but it took all the damage up to the point of being run over. The truck cracked it badly but did not crush or break it completely.
CON: Carbon can be scratched, it can be nicked and damaged, if fully cracked or broken, it can be repaired by someone who knows what they are doing but I would not recommend it.
Cared for Carbon, like many compounds is pretty durable long term. I personally have very well used carbon stocks that I have had for 16 to 17 years with a few nicks, scrapes, and hairline cracks that I repaired and are still running strong.
In scientific terms, Carbon is way F-ing strong and there is not better ounce per ounce product to build a stock out of.