Here's that age-old debate; It's been around almost as long as the ammo has. It may be cultural or "us vs them" in origin - German service handguns in both world wars were 9mm (Luger and P38) while the U.S. used the trusty 1911 - but I digress.
Penetration (how far the bullet goes) is only half the equation of a round's effectiveness. Permanent cavity (how much tissue it carves out as it goes through Sparky the BG) is the other. If penetration were the key, the only rounds worth anything for tactical use would be .22WMR and .17HMR, both of which are easily supersonic rounds and will go through several feet of ballistic gelatin.
There are valid points in both camps. 9mm guys say that a 9mm round, though lighter, is given more than enough energy to penetrate through the BG's entire body, and advances in hollow-point technology allow a 9mm to damage as much if not more tissue than a .45 while still penetrating. The .45ACP faithful maintain that simple is best; a 9mm round may or may not expand and no matter how likely it is to do so, there is always the chance it won't. A FMJ .45 slug doesn't NEED to expand to do massive damage to soft tissue, and it has the mass to shatter bone and continue past, still doing damage, where a 9mm, especially a hollow-point, is likely to simply lodge in the bone. In the case of hollow-points, a .45JHP will do yet more damage, however a JHP .45 does not have the impetus for the same penetration that a JHP 9mm would.
It all comes down to what you feel comfortable with, and also to cost. 9mm is cheap; most other handgun calibers are at least half again as expensive per round, including .45ACP. A 9mm also holds more rounds and kicks less than a .45 (these are dependent on comparative gun design; a compact polymer-frame 9mm is gonna have some upward oomph while a 1911 in .45 has more mass for less kick). This allows you to put more rounds into a BG in a shorter time (4-5 as opposed to 2-3, and fewer reloads if S really HTF). A .45ACP, if you can handle the kick, is a more massive round that does more damage per shot. This allows you to save some money over premium 9mm defense loads by spending $15 on 50 Winchester FMJs rather than $25 on 20 premium JHPs. (but the 9 still wins on plinking cost - target-grade FMJ would be $7/50 for white box). .45s also generally are arranged with single-stack magazines resulting in narrower grips, making them better for concealed carry and smaller hands at the cost of reduced capacity. This isn't always the case; the Glock 21 and 30 have staggered mags similar to a 9mm, giving 15-16 rounds of .45ACP goodness per mag (10 in the 30's compact mag).
9mm Luger ammo predates WWI (almost 100 years of military service), and serves a large portion of civilians, LEOs and now the U.S. Army. It's good enough for government work (literally) and many people trust their lives to it. .45ACP is also a venerable cartridge, and for over 80 years U.S. soldiers refused to have anything less on their hip. Many LEOs still use it, and 90% of the gun shop employees I've seen who carry in the store sport a cocked and locked 1911 in .45ACP.
In short, pick one and get good with it. Either round, used effectively, will persuade Sparky to cease his criminal activity and crumple to the floor with frightening speed.
