The issue isn't between handguns and shotguns, but between two handgun calibers. The .357 packs an astounding punch, and it does it out to respectable distances and to fairly large-sized critters. The 125gr JHP can, and has, put down deer and, yes, Virginia, even bear and cougars. It's also been shown to remain in human bodies, which means it's able to transfer 100% of its energy. It's also been proven on the street, as has the .45.
Bottom line: the .357 has been shown to have a flatter trajectory and to put down deer-sized game. The .45 has a much more limited trajectory and is not deemed suitable for hunting deer. Whether it tends to stay in the human body I don't know, but given the above, it should be considered not quite the stopper the more powerful .357 is.
If the bullet is a 185JHP, and the load is a +P, well, this might be different; for conventional loads, however, I'll take the .357.