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.
16 Pistols, 5 Rifles, 1 Shotgun, no time to shoot them