Okay, a few historical notes.
The US Army at the dawn of the 20th century switched from the Colt SAA .45 to a double action .38 and it did not fare well against the Moros. The .38 they were using was basically what we know today as the .38 Colt or .38 S&W. NOT the .38 S&W Special. From memory, its ballistics are roughly somewhere around that of .380 ACP. They switched back to the .45 Colt. The .45 ACP, one of the first smokeless powder cartridges,was designed from the blackpowder .45 Colt.
The Mauser 96 and the Borchardt were the state of the art for semi-autos then. Good designs, but bulky. Winston Churchill carried a Mauser in South Africa during the Boer War.
Also at the dawn of the 20th century, JMB was designing all manner of small "pocket" pistols in light calibres. Remember that this was also the time when the first smokeless (nitro-cellulose) cartridges were being introduced. The target market for these guns were the upper classes of society, bankers, business owners, etc, who felt threatened by the high crime rates of the day (urban environment, poverty, etc.) The intent was "conflict resolution" at knife point distance. Calibres were generally .25, .32, & .380
Larger guns and calibres soon followed. Revolvers were beginning to be viewed as antiquated. Some countries, notably the USA and Germany in particular moved to the more advanced "self loaders". Hence 9mm Luger.
Europeans and Americans took somewhat divergent paths at this time. The Europeans found the smaller (.32 to 9mm) calibres adequate for law enforcement and military use. The US military accepted the .45 and never looked back until WWII. Law enforcement moved to the more powerful ".38" cartridges of the first half of the century -- .38 Spl & later, .357 Magnum. Somewhat ironically, the majority of US law enforcement agencies kept the .38 Spl into the late '80s.
Why the divergence? European police engagements were almost exclusively in densely populated cities and over-penetration was an issue even then. Their collective experience showed that the calibres were performing adequately.
Jump now to WWII. 9mm versus .45. Given the collective experiences of the combatants 9mm was chosen by most countries after WWII. Australia, Canada, the UK issued 9mms in limited quantities during hostilities, but only made the switch official AFTER the war. Curiously, Canada which issued .45 Colts during WWI, and to its paratroopers during early WWII, was the first to move to the Inglis 9mm.
Why did the US stay with the M1911? Literally hundreds of thousands of 1911s were in US arsenals along with Millions of rounds of ammunition. It was too expensive (fiscally imprudent) to change. It's much the same reason the M1 Garand was chambered in .30-06 instead of the cartridge John Garand designed it for. Mac Arthur made that call.
Jump now to the 1960s. Europe, particularly Germany was in the throes of urban guerilla warfare. Bader-Meinhoff, et al. Many of these urban terrorist groups had at least limited logistical support from the Eastern Block, much of it channeled throught the DDR. German Police soon found themselves facing fanatical, Marxist U.G.s armed with better, more modern weapons than the mostly pre-war Walthers filling their holsters. Munich sealed the deal. 9x19mm was the choice.
An earlier poster mentioned the FBI Miami shootout. He correctly stated that the outcome was the result of bad tactics. Rather than even confront the possibility that its training and tactics may have resulted in the deaths and injury of its agents, it scapegoated the weapons and calibres involved.
The FBI calibre studies that followed ended with the "Boo's" selection of the 10mm. Subsequent problems led to the development of the .40 S&W, which many big name gunwriters of the day called "Forty short and weak". Interestingly, the .40 is now the darling of US law enforcement.
What's the answer? Well, what's the question? If it's what calibre is best, then there is no right answer. If it's what works, then the answer is all of them, BUT you have to do YOUR job first.