Can't comment on the rimfires, but the centre fires seem to be more of a marketing ploy than a genuine benefit. "Spend more money on the next big thing!"
Played with a few of the first gen models, mostly the Rem 700 carbon. The repetitive heating and cooling eventually separates the barrel from the carbon wrap. The carbon wrap also starts to chip and flake quite quickly.
If the process were as beneficial as Christensen Arms indicates, then the other manufacturers would all be pursuing further development. The reality is that they toyed with the idea 20 years ago, realized it was a flop, took brief advantage of a niche market, then shelved the idea next to Beta and 8track.
I don't think much of the concept of carbon barrels, however I do believe that Kifaru was on the right track with their lightweight rifle, by wrapping only a small portion of a skinny barrel to add just a bit of additional support to dull barrel whip. But, even the Rambling Rifle seems to have gone the way of the Dodo and what remains is the standard, skinny barreled, short action cartridge, occasionally in a modified receiver and a fiberglass and graphite stocks.
The Rem Mountain LSS and the Sako Finlight dropped into quality stocks are likely the most common choice. I doubt the carbon barrels will find any more success than these off the shelf choices.