No pistol cartridge is adequate for personal defense. The most common response when a person is shot with a handgun is to RUN AWAY. They all suck. Using a pistol for personal defense is picking the one that sucks the least. We use handguns because the vast majority of the time, it isn't feasible to carry a long gun everywhere.
Having said that, just for fun, run a search for threads in here (some moderator nazi will probably yell at you for asking this question without looking through other threads first,) and see that we have been arguing about this for the last 100 years. (Literally.)
Remember that the original 9mm Luger pistol was actually chambered in a smaller, bottle-necked 7.65 mm. When the U.S. Cavalry tested it, they wanted to see a bigger round. (They were carrying revolvers in .38 and .44 caliber at the time. So, they tested the same pistol in a shorter, rimless .38. (Actually .355, but that's another endless argument.) America bought the 1911 (.45 ACP) instead. Germany fielded the Luger and later the Walther P-38 also in 9mm.
Any defensive round, 9mm or larger, WHEN USING GOOD JHP (jacketed hollow-point) AMMO, will do the job. Splitting hairs and measuring stoppage percentages has little to do with real life. I USED to draw the line at .380, (which is a 9mm just a touch shorter and less powerful) because some people want or need very small pistols. But now, since you can get fantastic sub-compact pistols in 9mm, .40, .357 Sig, .45 ACP, or .45 GAP, just to name a few, I really can't see where a .380 is the 'best' choice in any category.
I am issued a 9mm pistol for duty, and my main problem with it is, we are issued a terrible load for it. (115 gr, fmj, 'full metal jacket') When comparing effectiveness between pistol loads, it's pretty much at the bottom of the list. By comparison, PLENTY of lives have been saved by 230 gr .45 ACP in FMJ. Much larger bullet, much lower velocity. As a civilian, I carry a 1911 with 230 gr, premium jhp ammo. When the choice is yours to make, you should give yourself every possible advantage.
I tell my friends, buy a 9mm if you want to. (Higher capacity, lower recoil, cheaper ammo.) THEN, take it to the range, get some instruction, shoot at least 1000 rounds through it, (including 200 rounds of the load you plan on using for defense,) and make sure you really know how to use it. THIS is the part that saves your life, not .45 vs 9mm.