I'd be interested to hear why you think the person with the gun/plate will feel more recoil?
Because it is my belief that peak recoil force (and not total recoil energy) is the most important factor in determining how much a shot hurts. And since the bullet accelerating (decelerating) into the plate happens so much faster than the acceleration of the bullet out of the barrel, the peak recoil force will be much more.
I in part believe this as a result of skimming a bunch of articles on the effects of padding in injury prevention. Where you find statements like these.
For effective prevention of impact injuries, any protective
device should attenuate the peak impact force
from
Kyu-Jung Kim, Ali M. Alian, William S. Morris, and Young-Hwa Lee
"Shock Attenuation of Various Protective Devices for Prevention of Fall-Related Injuries of the Forearm/Hand Complex"
Am. J. Sports Med., Apr 2006; 34: 637 - 643.
I have a bunch of such articles marked, now that my semester is over I hope to be able to get to them (except that it is hunting season, so maybe it will really not be until summer.) I cannot state confidently until I read some more, but I think that the literature shows that soft tissue damage in impact injuries involves thresholds of peak impact force. So as long as the peak impact is kept under a certain amount the total energy is less of an issue. This is why even very small changes in peak force(near threshold points) might result in a markedly different experience for the person receiving the impact....