It is proportional to the energy (but also depends on the nature of the collision &c &c)
Here's an example of why. Let's consider the kind of case proper physicists spend all their time thinking about: giant asteroid impacts (even now, teams of mad physicists, all played by Peter Sellers, are working out how they can steer some asteroid to collide with the Earth thus rendering all non-mad-physicists extinct).
The thing that makes these really bad is heat: when some large meteorite collides with the earth it's not the case that the Earth gets knocked out of its orbit and falls into the Sun, or gets thrown into outer space, or that the impact is so violent that everyone falls over or something (I have no idea what the seismic effect of the K-T event was, but I do know that it wasn't what did for the dinosaurs). What causes the problem is the abrupt release of a very large amount of heat: about $10^{23}\,\mathrm{J}$ of it. This caused some pretty spectacular events. There is dispute as to whether the impact caused the entire terrestrial biosphere to catch fire, but, well, there is dispute about it: it may have done that.
But you can't turn momentum into heat: momentum is a vector quantity and it's conserved: all you can turn momentum into is momentum. What you can turn into heat is kinetic energy. So it was not the momentum of the Chicxulub impact which did for, well, pretty much everything, it was the kinetic energy.