9mm is, in my mind, the semi-auto equivalent of the .38 Special in that both are at the bottom end of what can be considered an adequate service-class cartridge (one that can be trusted to both expand reliably and penetrate adequately with hollowpoints). Both cartridges have benefited greatly from improved bullet technology and can, with the right loading, deliver very good terminal performance. However, both cartridges require the user to be somewhat picky about load selection because, while they both have excellent HP loading available, there are still many very poor HP loadings being sold for both cartridges (neither is a cartridge I'd trust with generic WWB, UMC, or American Eagle JHP's).
Now, if all else is held equal (shot placement, recovery speed, magazine capacity, quality of bullet, etc.) I think that larger and more powerful cartridges like .357 Sig, .40 S&W, .44 Special, and .45 ACP are probably more effective than 9mm or .38 Special, but all is very rarely equal and the difference is small. Both 9mm and .38 Special are extremely efficient cartridges in terms of terminal effect delivered for recoil produced. From a medium or large frame handgun, both 9mm and .38 Special are very easy for even a moderately experienced shooter to handle and, in general, require less trigger time to master than larger and more powerful cartridges.
Likewise, while bigger cartridges cause somewhat greater tissue damage, the difference IMHO is not particularly significant as, with modern ammunition, all the service-class cartridges are designed to do about the same thing: penetrate 12-14" and expand to 1.5-2x their original diameter. It is not until you get to the magnum-class cartridges like full-power .357 Magnum, full-power 10mm Auto, .41 Magnum, or .44 Magnum that terminal performance is substantially different, but these cartridges usually come at the price of substantially more recoil and/or larger and heavier guns.
The largest advantage to the 9mm, in my mind, is its cost. For the non-handloader, 9mm is the cheapest centerfire handgun ammunition available. Even as a handloader, I've never had any interest in reloading 9mm ammunition because, even at today's ammo prices, it's just not expensive enough to be worth the time and effort to load. With a 9mm, most people can afford to practice more and skill with your firearm, IMHO, is much more important that caliber, velocity, energy, bullet diameter, or much of anything else.