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; 92FS; 92S; 8040G | Rock Island GI 1911 | Sig Sauer SP2022; P6 | Colt Python 4"; 1968 Detective Special 2"| Smith & Wesson M642 No-Lock | Ruger LCP; 10/22 | Daniel Defense M4V1 | Remington 870 | Alpine M1 Carbine | Steyr M1895 |1943 Izhevsk Mosin M91/30 | Walther PPS