The crumple zone absorbs kinetic energy / momentum and allows a smoother and slower deceleration for the passengers as the energy transfer of the impact gets drawn out over time. The suddenness of crashes is what causes the greatest injuries, so you want it to be less sudden.

If both cars have equally performing crumple zones then both zones contribute equally to this "jerk reduction" (a rapid change in acceleration is called jerk), but if only one has it then you only get half as good reduction and the slowdown will be more sudden.