Damage to the car will depend on how much of the original kinetic energy of the car is absorbed by the car (and how its structure reacts to this energy) vs how much is transformed into other energy. Kinetic energy equals 1/2 times the object's mass, times it's velocity squared.
So, if you have a car moving at 55 mph hit another car head-on moving at 55mph and both cars stop moving completely as a result of the crash, each would absorb its own initial kinetic energy as damage (which would be just dependent on its mass and initial velocity of 55 mph).
If you have a car hit a brick wall at 55 mph and is completely stopped by the wall, it would absorb its initial kinetic energy and have the exact same damage as the cars hitting head-on. (This is assuming that the brick wall is so sturdy that it does not absorb any of the energy during the crash).
If you have a car moving at 55 mph hit a brick wall and bounce off of it with all of the kinetic energy transformed into it bouncing backwards, then there would be no damage to the car at all.
If you have a car moving at 55 mph hit a stationary car, which then bounces off of it, with the first car transferring all of its kinetic energy into the kinetic energy of the second car, there will be no damage to either car. (completely elastic collision)
If you have a car moving at 55 mph hit a stationary car and the stationary car bounces off of it and the original car bounces back some too, there will be less damage to the original car than if it hit a brick wall.
Etc, etc.