Title says it all, really.
Because you can fit more 9mm rounds into a magazine than you can .38 rounds.
.38 is typically a revolver cartridge, typically with a 6-shot capacity.
9mm is ballistically similar but the cartridge is much shorter, meaning it’s ideal for auto-loading pistols like the Browning Hi-Power or the Beretta M92 as you can get quite a few cartridges (13 and 15, as a general rule) into the magazines of these two guns respectively.
Power-wise, the 9mm has a higher muzzle velocity (1100 feet per second or thereabouts), against the .38 Special’s c. 980fps .
The main advantage the .38 Special cartridge offers nowadays is that they will shoot perfectly well out of .357 Magnum revolvers, which cuts your ammo costs down.
You wouldn’t want to be on the wrong end of either a .38 or 9mm bullet, though…
I don’t know that it is, to be honest with you. Both are on the low end of what are considered adequate self-defense rounds. The difference is really in how many of each you can carry in each load. .38 Specials are generally limited to 6 rounds, whereas 9mm Luger (Parabellum, whatever your fancy)-chambered weapons can carry up to 17 in a standard magazine, with a ludicrous 33-round magazine option for 9mm Glocks.
If you check the specs, you’ll find that 9mm has more energy and muzzle velocity than .38 Special in pretty much all cases. Some people prefer slow and heavy, others prefer fast and light. There are compromise loads for each, of course.
Last, 9mm has become the military standard for sidearms, and it’s what people are more familiar with as a result. .38 Specials can be fired out of a .357 Magnum revolver which gives it a bit more flexibility, but it can’t overcome the load limitations or the perceived lack of adequacy.
EDIT: Simulpost! Thanks for stealing my thunder.
Hijack -
Wouldn’t you have to readjust your sights for the different load?
It does adjust the point of aim, but the adjustments are generally Kentucky Windage adjustments. .38 Specials hit low compared to the .357 Magnum out of my Ruger for me.
Most revolvers have fixed sights, and those that don’t are sighted in for the load that is intended to be used most often, so the adjustment is all eyeball. Otherwise you’ll be chasing your sights all over the place for every different load, and that sucks.
Sorry, I was thinking in rifle terms. I guess that at the ranges pistols are used, the difference wouldn’t really be noticeable.