Lennard Zinn queries manufacturers of carbon parts about their damping ability. I don’t buy into the idea that carbon bars/seatposts/cranks improve comfort, which seems to be founded on the idea that carbon damps high frequency vibrations. That may be true on a test bench, but there’s no evidence that high frequency damping makes any difference on the road. And, carbon’s stiffness would seem to eliminate any advantage when the bike takes a big hit.
The right tires would seem to make a bigger difference.