They are only lighter. They will also have less whip. I'm not sure I buy into the heat dissipation claims.
I was helping with R&D for a carbon company for snowmobile parts like handle bars, backers, hoods, and anything else. According to the carbon they were using its roughly 10 times stronger than steel for the same thickness. That would mean less whip in the barrel. Does that mean they are more accurate? More than likely no. As I've seen some amazing steel barrels. So either the whip doesn't hurt as much as you would like to think or they just don't whip as bad as you think.
Here's why I did a carbon on my 6.5 creed. I was looking for the lightest weight rifle I could build and still be accurate. And not just for one shot. So I did carbon. I also have a pencil thin fluted 6.5 Grendel I have for shots under 300 yards. First cold bite shot is always where I expect so for hunting it's not a big issue.