Long version: (Sorry, I can't really make this not seem technical without taking too many details out and making my description wrong.) According to scattering theory in particle mechanics, the momentum-transfer cross section describes the radiation resulting from a collision -including particle radiation and the deflection of particles in the material of the target. Depending on how elastic of a material the target is it can absorb different amounts of kinetic energy before shattering or tearing and may even return to its original shape, but that deformation is a kind of wound itself in a living target. The deformation and the type of injury caused is irrelevant, though. The important thing is that more momentum means more damage to a living target in almost every instance. The damage is caused by a force -and therefore energy- but using the kinetic energy of the projectile to model impact force neglects the fact that elastic collisions do not conserve energy and that every collision is elastic to some degree. There are a few instances where a very larger cross sectional area, an impact at a very acute angle relative to the target, or a collision that occurs over a longer period of time will affect the momentum transfer, but they don't apply to us. A projectile's momentum at the time of impact is the best way to quantify the damage caused by a projectile without actually trying to calculate the damage. And I don't want to try that, it's doctorate level mathematics.
Shorter version: There's a math theory that describes how radiation travels after a crash. These radiating waves are what cause damage to a target and they're mostly cause by the momentum of the projectile. We don't live in a perfect world and that sometimes isn't enough to describe the damage all by itself, but we luckily don't have to worry about that to have a functional model. Plus, the math for that is over my head. The projectile with more momentum will be the most physically damaging.
Keep in mind, dead is dead and "more dead" is still just dead. The math doesn't say whether a small, fast projectile will break the skin or whether a large, heavy one will cause internal bleeding. This only models straight tissue damage.