The .45 ACP is a superior round. It hits harder and larger. The 9mm makes up a lot of the ground with capacity and short follow-up times, but the .45 is a better round if you only had one shot.
That said, modern JHPs are superb and I would feel very well armed with a 147-grain HST or Gold Dot.
I'd narrowly pefer the .40 or .357 Sig over either for police duty since both the 9mm and .45 have - based on the research I've seen - a slightly higher tendency to glance off barriers.
Beretta PX4 Type F Fullsize .40 S&W | Beretta 92FS 9x19 Para | Beretta 8040 Cougar Type G .40 S&W | Rock Island Armory GI 1911 .45 ACP | Sig Sauer SP2022 Stainless 9x19 Para | Sig Sauer P6 9x19 Para | Colt Python 4" .357 Magnum | Colt 1968 Det. Spec. .38 Spc. | Ruger LCP .380 ACP | Daniel Defense M4V1 5.56x45 | Alpine M1 Carbine .30 | Steyr M1895 8x56 | Ruger 10/22 .22LR |1943 Izhevsk Mosin-Nagant M91/30 7.62x54R | Remington 870 12GA