OK, lets start with a basic understanding of the actual problem: Assuming sufficient velocity and penetration, unless the bullet strikes vital organs, systems or structures of the body, it doesn't really matter what caliber, bullet weight or velocity is involved. In short, your ability to place rounds accurately is more important than the actual cartridge or bullet you use.

As an example, the late great Jack O'Conner once placed a shot badly on a small antelope (gut shot it) with a .375 H&H. They spent about 3 hours chasing the poor critter before being able to put it out of its misery. Now, the .375 has been slaying everything from elephants on down for 100 years with great reliability when the bullet is properly placed. If a literal elephant gun (putting out 20 times the muzzle energy of a .38 Special) can't "stop" a 100 pound critter with a badly placed shot, exactly what do you think is going to happen if you fail to place your shots in a vital area with any .38 bullet?

So, find a load you can shoot accurately and practice, practice, practice. So long as you're using a good hollow point (although guns have been killing critters of various types for 400 years without expanding bullets) by a major manufacturer, you'll do fine-IF YOU HIT VITAL ORGANS, SYSTEMS OR STRUCTURES!

To quote an SAS training specialist: "We can argue all day if one is better than another if you get sloppy and put your bullets somewhere other than where they ought to go. What you can't argue about is that if you run out of bullets before you run out of bad guys, you're (deleted) dead!"