Damaging vital tissue sufficiently is what kills. Not energy dump. Sure, shoot a small animal with an energetic soft point and a lot of vital tissue is destroyed. If you are shooting something larger than a rat, then you need to hit specific organs. Before you can damage vital tissue, you need to reach it via sufficiently deep penetration.
Penetration and energy don't correlate in a linear fashion; depending on the mass and speed of your projectile. It also depends on if you are shooting flesh, sand, bone or wood. This little video uses an arrow to make that point:
Roughly speaking, "everything matters".
Other than the nature of your target and where you intend to hit it, you may need to take into account: 1) the mass of your projectile, 2) how fast it travels, 3) the shape of your projectile and its consistency, including all the material properties.
But an "often good enough" measure is the energy (combination of 1 and 2) of your projectile and its cross-sectional density -- this is part of the information in (3).
An exaggerated example: if you throw a bowling ball you'll give it much more energy than any .25 cal out of an airgun. But you likely won't kill anything because (2) its moving too slow and (3) the cross-sectional density is too low.
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