There's more than just material in regard to vibration damping/comfort. In regard to whether carbon handlebars or stems are more comfortable, not even the manufacturers agree. In a VeloNews Technical FAQ article Lennard Zinn posed the question of whether a carbon handlebar and stem combination would add damping and comfort, to ITM, Deda, Easton and Stella Azura - one said they would add comfort, but three said they would not (and suggested other ways to seek damping and comfort).
https://velo.outsideonline.com/road/...n-that-ride-2/
In a test done by Cervelo, they found there could be more compliance in handlebar tape than in the handlebars themselves. For example, a new tape called
OneTouch 3D by Prologo was features on several bikes at this year's Parix-Roubaix:
With the recent rise of gravel riding, several companies are making shock absorbing bar tape.