Once you hit 9mm and above when carrying modern hollowpoint rounds, shot placement and the ability to place those shots down range with the least amount of recovery time between each squeeze of the trigger is the key. If you can do that with a .45 more power to you!
(Image found here:
There's not a huge difference. A handgun is going to poke holes in a threat. The more holes poked the faster the threat stops. The only 100% guarantee for an instant stop to the threat is a shot to the brain or spinal cord. Anything else and the threat has the potential to continue fighting until they've completely bled out and their body shuts down. True 1 shot "stopping power" doesn't start happening until you move up to rifle calibers.
But I do love to shoot me some .45! It feels like a hand cannon!
Edit: P.S. As far as open carry is concerned, if you're gonna do it, at least get a level 3 retention holster and some weapons retention classes so you don't get knocked out and shot with your own gun. The presence of an openly carried gun can deter crime and probably will more often than not. But it can also make you the victim if you end up dealing with a determined and well trained or just plumb lucky criminal.
If you don't have weapons retention training and a level 3 holster, probably better to tuck it under your shirt.