This should be compulsory to all professional movers. If they offer Full value protection, that means that any damaged article will be repaired to its same condition before they received it. If not pay you or replace the article with a new one of the same kind.
If you find all of these in your professional mover then you might have found the best one! Always remember that your mover will be the one handling all of your belongings on the way to your new home. So finding the best professional mover is securing the safety of your belongings.