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 .40 S&W - Beretta 92FS 9x19 Para - Rock Island Armory GI 1911 .45 ACP - Colt 1968 Detective Special .38 Spc. - Ruger LCP .380 ACP - Daniel Defense M4V1 Carbine 5.56x45 - Ruger 10/22 .22LR - Remington 870 Express Tactical 12GA - 1943 Izhevsk Mosin-Nagant M91/30 7.62x54R