They both work. The trouble is concealment, ability to conceal/carry the load, & have accuracy.
For self defense I'd prefer armour and a shotgun or autoloading rifle but, the reality of my life means I need something that can go in a pocket or waistband & not be "made" EVER while doing physical work & activities.
Guns that small are tough to shoot in big bore calibers. To maintain accuracy (being able to keep all shots in a 2x3" box to at least 21 feet & an 8" circle at 15yd), conceal, & not be worn out physically just by carrying leaves you with ideal solutions of 9mm, 380, 38 spcl, & similar.
I personally prefer hollow points and have complete penetration with them in the above mentioned calibers.
That buck there had an arrow sticking out of him. He jumped up to standing from a thicket and lowered his head at my friend & his son, only 10' away. We were Turkey hunting with his son. The boy had the only shotgun loaded with #4 & a single shot. I took a few quick stumble steps to the side while drawing my p238 from my pocket loaded with remington 90 gr hp's and my buddy drew his knife (the only weapon he had). I fired two shots quartering towards & big boy dropped. Both shots hit him. Only the jacket from one was found in the exit side hide. The rest penetrated completely somewhat diagonally.
It was so close & it happened so fast I felt like the boy was in serious danger & did all I knew to.
A 90gr HP at 1k is not a friendly punch. The exit holes were 40 cal +. Typical self defense distances for civilians is inside 21'. That's fortunately, the only man sized thing I've felt as if I had to shoot in defense of my self or others. Would have prefered a vaporizer Ray gun in my hand when that buck lowered his head at them, when he took his step I fired what I had.
At that point I wasn't shooting to kill. I was shooting to stop the threat to the young boy & my friend. Anything more than stopping the threat is pre-meditation in the eyes of the law.
When I went to front sight they trained us to put two shots in the thoracic cavity. If that doesn't stop the threat you would need to be able to perform a fail to stop drill. One well placed shot up top. Don't know if I could have made that shot had he taken a second step their way but, that's where my sights went.
They say a man can cover 21' in 1.5 seconds. Can you draw from concealment and fire 2 where they need to be in that much time. If not your got. Drawing from concealment and shooting at timed turning targets is a bit different than something alive but, I'm glad we do it and feel like it made me more capable that day.
In self defense how you handle the gun matters quite a bit. As with anything the Devils in the details.