Both accidents are equal.

How hard an accident is for you, depends on how quickly you stop. In physics, this is called negative acceleration and in this case you suddenly go from 50 km/h to 0 km/h. The human body can only withstand a certain amount of acceleration, irrespective of it being positive (acceleration) or negative (deceleration). The acceleration you are being subjected can be felt as a force or weight, something we call g-force and measured in “g”.

During freefall on Earth, a dropped object will fall with a constant 1 g acceleration but will feel no force, until it splatters (ie. decelerates) against the ground. On the other hand, if you are standing on Earth's surface at sea level you'll have a force of 1 g constantly acting upon you. Reaching 5-6 g acceleration will cause most humans to lose consciousness (G-LOC), while higher acceleration can cause severe damage due to the internal organs being squeezed (or squished!).

In our example, the strength of the negative acceleration depends on how long it takes for the car to decelerate from 50 km/h to 0 km/h, which in this case is dependent on the size of the “Collapsible Zone” of the car. Given that both cars have the same mass and velocity, both impulses are equal and will be canceled out in the crash, causing the accident to be the same as if the car hit a solid concrete wall. See the pictures for more clarity.]