I'm not sure what caliber the OP is referring to ??
If you are on the .380 or .38 side of the selections with a short barrel, then ammo choice does become more important, IMHO. Those two calibers will struggle more with performance, but can still get the job done, due to velocity and bullet weight. With those as my choice I would tend more towards those ammo rounds that penetrate more and probably less on the expansion element.
When the caliber is increased and the bullet weight also, there are more choices to fill your own needs. At the .40 and 45ACP level I do pay attention to both penetration and expansion when looking at defensive shooting situations. Some HP can become clogged with clothing, more likely in the winter, and turn into penetrators supreme. But modern bullet design has some options that can handle the clothing issue, provide for very acceptable penetration, and have wonderful expansion for large wound channels. HST from Federal is an example of such a loading in many larger calibers.
I will be carrying factory ammo in my EDC shooters with a look for both penetration and expansion at the speed those loads can produce.
If I was in an outdoor hunting or defense situation against bears I would be looking for Hard Cast driven at fast as I can shoot accurately in a stress situation. I would want to penetrate and hopefully stop such charges quickly and would be using large calibers handloaded fast.
Lucky Gunner ammo seller has some interesting tests on ammo for penetration and expansion for many calibers with many choices of ammo for each caliber.
https://www.luckygunner.com/labs/self-defense-ammo-ballistic-tests/
