In self defense with a firearm, you are dealing with an immediate threat of death or serious injury. This means you absolutely need the firearm to go bang when called on.
I am only familiar with the 10/22 and while it is a good rifle, my experience has been that .22 semi-autos are very ammo sensitive.
However, assuming both rifles are equally reliable and you test your ammo selection, your next task is putting lead on meat. Which rifle are you more competent with? Which one can you manipulate in extreme stress? One-handed? With someone hanging on to the muzzle? Once you have training and handling issues down, you can start worrying about what happens to the person you shot.
There are basically two ways you stop someone with a firearm: psychological (Ow! That hurts! I do not want to be shot!) and physical (blood pressure drops to the brain and person becomes unconscious).
Psychological relies on your attacker's mindset and is not something that can be controlled reliably. To stop someone physically, you have to disrupt their central nervous system or cause a substantial loss of blood by damaging large, blood bearing organs. In order to do that, you need enough mass to penetrate to where those structures are located. Bullet design will of course play a role; but in general, 9mm is going to have an advantage here as well as make a bigger hole.
All of those aspects taken together will help decide what is right for you.