To start out, let me step back from the actual question to a more general description of collisions. Whenever things collide, it is helpful to separate what happens into two parts, of elastic and inelastic collision. An example of a mostly elastic collision (where the inelastic part is very small) would be the collision of two snooker balls. An example of a mostly inelastic collision would be throwing a ball of mud against a wall. The names give you a cue as to what happens: when the snooker balls collide, for a brief moment they deform due to the impact, but they are elastic (like a rubber ball, just harder) and thus bounce back to their original shape, pushing each other off in new directions. In a purely inelastic collision, all that initial deformation is not reversible, and so there is no bouncing.

So what you have been measuring by determining how far the car bounces back is essentially the degree of how elastic the collision has been. What you are after, however, is something different. You want a material to absorb the impact, or to cushion the impact. This is related to yet another parameter, the impact force. This is independent of whether or not the collision is elastic.For example, the collisions of a rubber ball, a snooker ball, and a steel ball with a cement floor are all quite elastic (they will bounce well), but exchange the floor with your head and your preference for what balls you'd like to test will tell you that the impact force - the amount of force exerted by the impact- is very different for the three. The high impact force of your car colliding with the cement wall may actually be responsible for the small bounce, in that it is large enough to force small dents in the wall or the car which are inelastic, like tiny mudballs to use the initial example.

So what you would want to do is to find a way to actually measure the impact force or to compare impact forces. This is a little tricky because that force only lasts for a very short time. An idea might be to change your setup in away to make the barrier the same for both collisions (have a foam side and a concrete side) but moveable, with a certain resistance that you will have to experiment with. The further the barrier is moved by the impact, the larger the impact force would be.

For a car, the crumple zone is what gets deformed, making the collision more inelastic. While of course you'd rather avoid car collisions all together, if they happen you want them to be mostly inelastic - rather than cars bouncing around like snooker balls. The aim of reducing the impact force will have to be balanced with practical concerns - you would likely have gigantic cars if their crumple zones were made from plastic foam, which can absorb less of a force per volume than, say, a steel framework.

A final note: I have avoided using terms like kinetic and potential energy in the explanation of collisions, since I am not sure if you are familiar with them. If you are, you may be able to apply them here by yourself, or you could pose that as another question to us.