Both the .45 and the 9mm are effective rounds for self defense. The .45 vs 9mm debate has been going on for years and years.
Bullet design influences each one's effectiveness. But all influences are overshadowed by bullet placement.
A .45 in the "wrong" place will result in the person still standing and being able to shoot back. A 9mm in the "right" place will drop them immediately.
What is the right and wrong place? Depends on the situation.
Neither the .45 nor the 9mm is a guaranteed stop or guaranteed kill.
There is also the influences of how the shooter can shoot the individual gun. .45 handguns are not the same as 9mm handguns and some shooters can shoot better with one than the other.
When I was shooting IPSA scores were downgraded when the shooter used the 9mm (at least they did about 20+ years when I was shooting in competition), but many shooters still choose to use the 9mm round despite this downgrading. Why? Because their shooting ability with the 9mm compensated for the scoring differences.
It is always better to hit with a 9mm than to miss with a .45
It is also better to shoot your target with two 9mm rounds than one .45 round
Double tapping with a .45 can be more difficult than with a 9mm, depending on the firearm.