Having owned and damaged frames of carbon and ti, my opinion is that the latter is harder to damage but more expensive to repair. It's not easy to cut, shape, weld, and align ti frames. We recently bought a custom ti stoker stem, and it took a lot of work to bend and align. It just happens that our local framebuilder is a very capable ti specialist. I've been told that it's just easier to repair carbon dents and fractured tubes (add more layers or cut and re-laminate).

It's significant that most hi-end mtn bikes are now made from carbon. Mtn bikes take much more abuse (jumps and steep, rocky terrain), and frame failures and repairs are much more common. Carbon is more popular because it's flexible (ie. unusual geometries), durable and easy to repair.