Dammit, now I have to come in and break this down or I won't be able to rest.
Force Applied = Mass x Deceleration.
True enough. This is Newton's second law.
If two vehicles of exactly equal mass collide at exactly the same speed
they will each come to a dead stop within a distance that is equal to
the deformation of the front of the vehicles.
This sounds like you're assuming an inelastic collision, in which the two vehicles squish together and stick that way. Cars don't crash that way; they bounce, often as not. (Actually, they move as described by the momentum of their combined center of mass, this being conserved in collision, and therefore the smaller vehicle usually winds up being kicked backward in a head-on; but if you think I'm retyping that equation this late, you're more nuts than I am.)
A heavier vehicle wins this argument because it has more kinetic energy
and will therefore apply more force even if speed is equal.
Incorrect, by Newton's third law. In fact, both vehicles will see the same force applied, but will react according to their individual masses; therefore, the average acceleration (or deceleration) of each vehicle is inversely proportional to its mass. In other words, a lighter vehicle sees higher acceleration, which can translate into higher forces on the occupants (via Newton's second law).
The other problem is that the smaller car usually has less capacity to absorb energy, which can mean it will be damaged more severely in a crash if it soaks up more of the energy in the crash. That isn't a given, though, since the energy absorption of each car depends on more than mass.
I'm copying a lot of this almost verbatim from my physics textbook, which is probably the first good use I've put it to in eleven years.
Net: heavy vehicle wins, period.
Yep, and there's data out there to back this up. Now will you please stop putting up wrong answers so close to bedtime so I can get some sleep?