It's been argued, discussed and talked about a thousand times. It comes down to individual cases. Giving two different people the same set of circumstances will yeild 2 different results. The difference between a 9,40, 45, 44, 357, etc is impossible to guess. The old idea that the most powerful weapon still has the tendancy to do the most damage, is still the most noteworthy, given everything else being equal.
I have found the 9mm to be the ideal weapon for carry. It is light enough that you won't leave it home. And can be shot accuratlly enough to put the rounds on target without fighting with the weapon.
And during a real gunfight there is too much going on to accuratelly fire at the ideal place to stop your target. You will be lucky to get a clean shot in. Once things slow down you may be able to re evaluate and shoot a cleaner shot, if you are still able to shoot, and the threat has not stopped.But getting that first and second shot is going to determine the result for the most part.
If you can shoot a 22lr ruger or baretta, with extreme accuracy, then that's what you should use. 2 or 3 quick shots to the head will end things fast. The problem lies in that hardly anyone practices with moving targets, like leading ducks or pheasent, you need to know where that head is going to be half a second from now.
A decent drill if your range dosen't have moving targets, is to use 2 lanes or a target holder with clips for 2 target holders. Then shoot from one to the other rapidlly as possible, aiming for the center, Back and forth, also if you can, allow the target to come back to the station and fire at it while it's coming twords you. At least you will get some practice with movement. Even better if you and a friend rent 2 lanes next to each other, and take turns moving the targets back and forth to simulte movement durin a simulation of someone closing in on you. Try it out, you may be suprised how it changes things.