It started life as the .38ACP and was chambered in several autos around the turn of the century. It didn't sell, and it died. In the thirties, Law Enforcement wanted a round that had better penetration than the .38spec, etc that they were using, and the old .38ACP was brought out and hot loaded. It became the .38 Super. They were chambered in the Govt Model, and had some success. Not a great amount, but enough to keep it around.
The .38ACP and .38Super can be fired in the same chamber, so there's the obvious danger of firing the Super in an old gun. There's not too many of those around, so it's not a big problem. You can compare the stats from the ammo company propaganda.
It's popular in competition where power factors matter. There's something about the power class of a cartridge, and you can load the .38Super to run in the same class as the .45 without the recoil, etc. I'm not up on that stuff, but it's a popular IPSC round.
Another big boost is overseas, especially Mexico. You can't own a gun in a military caliber in many countries, and the .38Super isn't a military caliber. So it does great overseas.
Accuracy will depend on the gun. The cartridge has a semi-rim. If the headspacing is done on that semi-rim, usually accuracy suffers (as most of the older Colts did). If it's headspaced on the case mouth (like any other auto cartridge), then thye usually as a pretty accurate round.
Ross