It does not make a difference, not in the way you're thinking. Source: Mechanical Engineer
Theoretical explanation:
The question asked about the OP is a matter of impact, which is force over a small period of time. In this sense, the only way that the two situations could differ is in terms of static/kinematic friction. If you use a well lubricated assumption however, then in a rigid body kinematics sense, the only things that really matter are acceleration and angular acceleration, provided that mass and moment of inertia do not change. Thus, whether you're comparing car to car as rigid bodies or split up one of the cars and it's wheels, a simple FBD=KD diagram shows that the force transferred between the two MUST be the same.
If you want to use work-energy method, it might seem like this doesn't line up at first, but it does. The PEs and PEw terms cancel out since (in basic theory) there should be no real change of potential energy. Yes, the energy side of the equation is larger in the case of higher velocity (1/2 mv2, or 1/2 Iw2, depending on whether you look at the car as a whole or just the wheels, whatever.), but on the work side of the equation, that isn't balanced out by a change in the force, it's balanced out in terms of the integration limits for dS.
Note that, yes, you can nitpick about friction, fluid dynamics, material properties, etc..., but that gets so complicated so quickly that it trivializes the question that OP asks, so it's safe to say that he was just wondering from a basic mechanics/rigid body dynamics standpoint.
To make this easier to understand, think about the earth you're standing on. Even if we use it as a static frame of reference, you have to realize that both you and the earth you live on are rotating and moving through space at absolutely insane speeds. If physics worked the way that /u/Ausares was thinking, every step you take would shatter all the bones in your body.