Hang on, I did a terrible job at wording the question and now there's a misconception over what it is I'm actually asking!
I wasn't asking what speed the cars would be traveling at upon colliding with each other, I was asking how much damage they'd sustain. I wanted to know if the individual damage received by two cars colliding at 50mph would be double to the amount a single car would receive upon colliding with a wall at 100mph (assuming that the wall had an absorbance factor of 0, that both cars were traveling in polar opposite directions and that both collisions occurred in a vacuum)
It was put to me that the amount of individual damage received in the two car collision would be
double to that of the car colliding with a wall at the same speed (due to the doubled speed of approach) but I disagreed on account of there only being 100mph worth of energy in the two car collision, which wouldn't accommodate for 200mph worth of damage. The misconception was due to me using the term "force of impact", hehe...
Anyways, case solved. Old Silver was right!