.308 is the Proper caliber MOST EFFECTIVE "defensive" bullet to use.

Would a .223 or a .308 bullet cause more damage, assuming they hit in the same spot on two different people? (I've heard that the .223 is harder to treat medically because it fragments more, is this true?)

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I am a retired surgeon, and have done a fair amount of trauma surgery during my career. There's truly no comparison to the Damage Done [by a .308] specially to Bone and soft tissue and solid organs between the 5.56 and the 308. The 308 with nearly three times the mass of a 5.56 has much higher kinetic energy. It's kinetic energy that ultimately causes the damage when shot. The biggest reason the military phased out the 30-06, and the 7.62 X51 in favor of the 5.56 is that it is a lighter cartridge and an infantryman can carry a lot more ammunition. The lack of kinetic energy and the inability to penetrate body armor is a major reason why the 5.56 cartridge is being phased out in favor of a higher caliber heavier bullet. Ultimately it all comes down to physics.