I've killed lots of critters with handguns. Sometimes "on purpose" because I was hunting for them with a handgun.
Other times have been more spur of the moment or "unplanned" like putting down wounded animals or dying livestock.
I know that what I am about to say may be mildly "controversial" for the nets. And of course mileage will vary.
But, I have a lot of experience with this subject, good and bad.
And based on that experience I will NEVER purposely carry a hollow point pistol round (to include "ballistic tip styles") when thinking I may need to kill an animal.
Semi jacketed flat points or hard cast flat point is all that I will run.
The above statement is NOT AS IMPORTANT when you are using a caliber that is "appropriate" for deer hunting with a handgun, although I do that anyway. Can you ethically kill a deer with a .44 mag with a HP? Of course. Do I carry flat points anyway? Yep.
When you use "sub-standard" handgun calibers the expansion you get is negligible and does very little to help you recover the animal.
You want TWO holes in the animal, and the rounder the better. You WANT penetration. You WANT the ability to break bone if you come in contact with it.
I will always carry the heaviest, fastest, flattest metplat round I can find in that particular caliber and that my platform will safely handle and that shoots to point of aim.