I now carry a Charter 44 Spl as a backup handgun for whatever long-gun I am using for hog/deer hunting. I know better than to try to handgun hunt with either the 44 or the 357 I used to carry for the same purpose. It has nothing to do with the ballestics of the handgun, It is a matter of my weak hands and unsteady handgun shooting. I use a long gun because I can steady it and hit what I aim at, whereas with a handgun my percentage of hits drops as the distance increases.
The 357 could do the job on deer, especially if it is in a lever-action carbine. The 44 mag would do a better job. But my Mini-30 and/or 308 Winchester will give me the confidence I need to take the shot.