By looking at the expansion and guessing what the .45 can do, the question arises, is the larger hole more effective?
There is an accurate answer, but it is one that people tend to dislike.
If we consider ONLY bullet diameter and limit things to just the service pistol calibers instead of considering everything from .22Short out of a handgun up to 700 Nitro Express from a rifle.
The larger hole has a higher
probability of damaging something important.
Case closed, right? Well, that answer leaves a lot unsaid.
If both bullets hit something relatively unimportant as far as incapacitation goes, then they will be essentially equally ineffective. If they both, for example, punch through a roll of fat, the fact that one is bigger isn't likely at all to have any impact on the outcome of the fight.
If both bullets hit something really important as far as incapacitation goes, then they will be essentially equally effective. If they both, for example, hit the spinal cord, or the brain, or one of the large blood vessels over the heart, the fact that they differ in size isn't likely to change how fast the person becomes unable to fight.
So what about the case where the larger one hits something important because it's larger that is missed by the smaller bullet. That's where you can see benefit of the larger round; but people tend to overestimate how likely this is.
And, of course, since bullet diameter is a tradeoff (you get it by giving up other things), one should also consider things like "shootability", "carryability", capacity, penetration, etc.