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Trouble is... You’re both right about different parts.

One part is this: a 30-06 bullet from a rifle hits a deer and goes all the way through. The damage is almost all from the temporary cavity tissue damage and the resulting organ failure of the (hopefully) heart/lungs or at least quick hemorrhaging. The bullet barely slows down in the deer, so it leaves the deer without imparting as much energy into the deer.

A .45 is a fat slow bullet that tends to stop in the first big thing it hits. Not always... But often. All of the energy from a .45 that stops is more than the energy of a rifle bullet that doesn’t. No, it won’t throw somebody back. Neither will. People that get shot tend to just fall down.

But a “feature” of bullet-resistant vests is that the wearer trades penetration for energy transfer. A bullet stops faster and in a shorter distance on the vest than even if it hit flesh. Energy is transferred fully and over a very short time. It actually hits the wearer harder, but that is exchanged for penetration. Usually... That’s a good trade.