People spend WAY too much time parsing out differences between those rounds. But the answer is that there's no such thing as "stopping power" or "knockdown power";
I'm not sure the above is true, however I know of no one that would wish to be shot with either 45 or the 9.
I recall reading about the Philippine-American war and our troops were using 38 pistols that were failing miserably to stop the enemy.
They called back into service the SAA 45 Colts and they were stopping the enemy.
I believe this is what led to the development of the 1911 in 45 ACP caliber.
Now as for stopping power or knock down power even if they don't exist, there is a thing called power factor, which is what I go by
Power factor of a 115 gr 9mm FMJ bullet moving 1180fps is 135.7, power factor of a 230 gr 45 FMJ bullet moving 850 fps is 195.5, I'll take the 195.5 any day.
That does not mean I'll not carry a 9 or other smaller caliber on occasion, however I do carry a 45 the largest percentage of the time.
I always tell those that ask me, carry what you shoot best and practice with it often.