Very entertaining thread!
I'm not a physicist nor a mathematician; strictly a layman. And my layman's understanding is that some of a bullet's energy is expended during flight due to air resistance, and it doesn't "hit" as hard because its shape and frontal mass are so narrow that it punches through its target rather than transfering all its retained energy directly, as it would if it flattened so completely that it didn't penetrate the surface. Which is why there is so much discussion of bullet expansion, and wound channel, etc.
And think of the retained energy of a rifle bullet that passes completely through its target and travels on; the shot that kills the second deer after passing through the one standing in front certainly didn't transfer all its energy to the first deer! I've never been in combat, and hope never to be. But persons I know who have say that men who are shot by bullets drop; they aren't thrown back.
So my layman's answer to the OP's original question: No, the impact of being hit by a bullet isn't the same as the recoil felt by the shooter.
Cogito, ergo armatus sum.