Are carbon fiber speaker cabinets inherently better than wood or metal ones

It’s a custom designed material used as an alternative to wood so probably inherently better suited for the task. Wood is wood.

But either way can work well if done right. Done right usually cost somewhat more.

Is that what KEF uses in their LS 50s, Blades, etc? I don’t think so but a big thumbs up whatever it is they use. I do not miss the wood there.

The Blades were initially intended to be made of carbon fiber but they switched to fiberglass, probably due to costs and degree of difficulty 

Carbon fiber resonates at an extremely high frequency which are very easy to control and isolate and direct away from the large and very thin drivers. You have to know what you are doing however. 

Carbon fiber in a wet layup application would be absolutely awful in this type of an application.  Now if one had a cabinet design and a mold so that this process could be accomplished using an autoclave, or vacuum forming utilizing a  prepreg carbon Kevlar weave in multiple layers, final finishing layer in straight carbon fiber with a 2 stage urethane finish, it would look awesome. Not sure about the sound though. 

To @sounds_real_audio point fiberglass would be 1/3 the manufacturing cost. Can be blow-molded or autoclaved. 

It can be difficult to grasp the true benefits of carbon fiber as used to make speaker cabinets. Perhaps the stand out feature is that the low bass back waves off the larger drivers moves through the carbon fibers at a very high rate of speed and with the fibers correctly aligned will be directed away from the thinest part of the cabinet, the cone.  The fibers vibrate ( resonate ) at an extremely high frequency. 

Not sure what good this does? Well if you have a nice wine glass give it a ping. Now simply touching the glass with your finger quickly dampens the sound. This demonstrates how composite cabinets work best. The composite material does not have to be any high tech product, rather simply a material with a difference resonance point. 

The most cost-effective way to reduce enclosure and/or panel resonance is to brace like Hell. Look at the bracing Jim Salk uses in his subwoofer enclosures (into which he installs the Rythmik Audio 12" or 15" DIY kits).