Get a timer. It can be real.
No doubt in my mind it is real, for
some people. My point, in this case is that if it takes a timer for me to notice the difference, then there is no practical advantage in speed, FOR ME.
Best measured "time" I ever turned in was 9 rounds of .357 MAG in 4.37 seconds, at a local bowling pin shoot, decades ago. Didn't even come close to placing 3rd.
Games where a .1 or .2 difference in time decide the winner are outside my abilities these days. Also games involving shooting and the run, dodge & jump.
Lots of people say the 9mm has less recoil, and faster recovery times, but I don't see it, for me. Therefore, it's of no concern, to me.
The 9mm having a large capacity advantage over the .45 is another thing, one that depends on just what it is you are shooting. I have four 9mm pistols, three of them hold ONE more round than my 1911A1 (8 vs. 7). The other is a single shot!
No, I'm not typical, I suppose, not that it matters. All I'm saying is that the "hard and fast" advantages of the 9mm are not universal.