Whenever an object strikes a stationary object of equal mass, what happens is that there will be equal and opposite changes to the momentum of the two objects. That said, it will be wrong to think only the stationary object will experience a higher momentum change.
According to the law of momentum conservation, it states that; the total momentum of two bodies before collision will remain the same after the collision, provided the collision occurs in a closed system. However, this does not mean that the momentum of each colliding object will not change.
The law states that even if the momentum of each colliding object changes, the total momentum of the two objects will remain the same. This happens because, in any collision, each colliding object will exert equal and opposite forces on each other. This rule still stands regardless of the nature of the collision.