This is a complicated subject in part because barrel length also needs to be considered as well as distance from the target. Paul Harrell did a very good You Tube comparing .22LR to .25 ACP using Beretta tip ups. The results were almost identical. Given the centerfire is more reliable that the rimfire, the choice
in those guns has to go to the .25ACP, but, i
n a longer barrel, the .22LR would have superior stopping power.
Given that these guns are designed to be "get off of me guns" and that the end of the barrel is intended to be pushing into the flesh when fired, both the .22LR, or even a .22short, and the .25ACP should be one shot stoppers when planted in the brain pod.
I have carried as backups, both a NAA .22LR and a Seecamp .25ACP at the same time. They are small and very easy to hide, even in a bathing suit. During most of that time a .45ACP was the primary gun. The smaller calibers do have a place.
If numbers were available, I would love to see stopping power results between an XDs in .45 ACP and a Hellcat (9mm) or similar short barrel guns. I'm sure I'm just dreaming however. Real shooting results are hard to come by.