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Shoot both equally well, double taps at 6- 7 yards on 6 inch circles.
As an instructor, I'd wish to observe the results of you doing the "double taps" and see if the 6" groups are the result of the second or first rounds opening up in placement, in a consistent manner, that could be corrected with some work on grip, trigger press or reducing anticipation of the recoil, meaning how well you're able to control and run either caliber gun, in general.
I'd have you compare the results of some varied and demanding drills, comparing how you felt while running the guns, as well as looking at both "the clock" and the results on the targets, and suggest you choose whichever pistol you felt gave you the best potential to effectively handle and control it, while making consistently accurate hits, no matter the number of shots fired, under stress.
Both the pistols you mention have an ample, and similar, number of rounds in their magazines. The extra velocity & M.E. of the 10 may not be as much of an "advantage" as expected, and might even be costing you a little when it comes to your consistency of controllability, especially as you start to push/reach the limits of your existing skills.
I've seen my fair share of folks bring both calibers through qual courses-of-fire over the years. Seldom has someone been able to run their 10 as well as they could another caliber (like .45 or .40), especially when they experienced the normal self-induced stress of being watched by one or more instructors, as well as by other students/shooters.
You might be the exception, which is fine. It's your life you're planning to stake on the difference. You only have to convince yourself which "answer" is the right one for you.
Just because you might be able to run one caliber a little bit faster than the other, the amount of "faster" might not be something that seemed critical to you. Your call.
Me? I'd take the .45 over the medium-bore 10mm, even as a long time Magnum revolver shooter who doesn't mind a little increased muzzle blast and rise.
I actually had the opportunity to shoot the first G20 that, according to the Glock rep in '90, was the first one imported into the US when the model was just arrived. He provided Norma ammunition for it, which was somewhat hotter than originally envisioned for the 10mm Auto, remembering what Cooper wrote that he thought would be the best personal defense loading for the caliber. (Remember that the .41 "Police" load eventually developed for the .41 Magnum was a heavy bullet loaded to lower velocities, too.) I remember thinking that it was soft-shooting gun for a medium-bore pistol, but still preferred the .45 for it's recoil impulse, myself. I haven't changed my mind over the years in that regard.
That's me, though, and you only need to please yourself.