I think that was an excellent question, although it may be of more historical interest now than of practical value, referring here to revolvers and hit ratios. I've also seen the question brought up before.
What I've read suggests that revolver-armed policemen fired more slowly, though I don't recall if their results were any better or not. But what is interesting, if you go back far enough, is the variety of shooting methods officers have been taught to use. While one-handed shooting was usually assumed, two-handed shooting stances were expected to be used "when necessary" even before WWII. The one-handed style probably still dominated the customary combat positions for a long time. Even that was often what we call "point shooting" sometimes, even in big city departments where there actually was training.
It is also interesting to note the influence of shooting games on real-world self-defense training, for better of worse, although I'd have to say it has more recently been more positive than not. In the late 1940s and 1950s, Western style fast draw was even seen to have some value for real world application. That very fact should make you think twice about the value of contemporary shooting games.
Finally, Fairbairn, in his book "Shooting to Live" stated that the more his gun resembled a machine gun, the more he liked it.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.