Well mass and high-temperature behavior are really the key benefits with carbon/ceramic brakes.
Their high temperature properties make them more dependable during heavy use as they barely suffer from brake fade, they are also not prone to warping due to carbon fibers extremely low coefficient of thermal expansion (CTE). The CTE is actually negative :)
Reducing the vehicles un-sprung/un-dampened mass improves handling.
Reducing the total mass is generally desired in most vehicles, the reasons are many.
Reducing the wheels moment of inertia improves handling.
Wear: They will last much longer than steel discs. However considering their much higher cost, compared to steel discs, they are still more expensive in the long run.
Chemical: Another benefit but I would not call it key is that they are basically inert. They will not corrode. No more rusty discs.
Price: They are expensive compared to steel, however compared to carbon/carbon discs they are cheap and still offer many of the benefits.