I think a fair portion of the answer to this question depends heavily on the closing speed of the two cars. For simplicity, spherical cow style, assume equal crumple zones fore and back that are equal on both identical cars. It then stands to reason that approximately half of the energy of the impact will initially be absorbed by each car. Kinetic energy grows with the square of the velocity, which in this case is going to be the relative speed at impact. (If the car behind you is braking or if the front and rear of each car don't have equal crumple zones, it gets more complex very quickly.) The kinetic energy of a collision of any kind at even, say, 20 km/h is hugely different from that at, say, 5 km/h. Assuming that the car being hit rolls freely (no braking, is in neutral or equivalent), then the brunt of the kinetic energy of the impact seems likely to be either taken up by the crumple zones or result in a forward acceleration, which absent braking must go into friction.

If the front car is braking, that mostly changes how quickly the forward motion is converted into friction, because the brakes are designed to induce friction and the weight of the car in front would then be resting on mostly static wheels. (ABS may or may not make a difference here.)

There is also the issue of the jerk (by which I mean not the driver behind you, but the rate of change of acceleration). The initial impact is going to propel the front car forward, pushing the seats toward the occupants' backs. Being stopped from the front, as happens to the rearward car, is going to propel the occupants forward; they are going to hit the seatbelts (hopefully before moving too far) and then be thrown back toward the backs of their seats (all relative to some point in each respective car). This seems unlikely to have much of an effect on the total forces involved, but if the forces are great enough, it can very well make a very real medical difference for the occupants.

Oh, good point -- I should have addressed speed. I'm assuming there's a spectrum where at one end it doesn't matter (too slow to be hurt) and at the other end it also doesn't matter (you're dead either way). I don't know what the "could make a difference" range is, but to keep this question from being too broad, I'll edit for the city-driving case that prompted the question.