The .38 super did achieve considerable popularity, albeit briefly. It's popularity came from the fact that it was one of the hottest rounds available when it was introduced, and it quickly gained a reputation for offering superior penetration of light barriers, which made it very popular with law enforcement, who wanted a gun capable of shooting through auto bodies, which their .38 revolvers wouldn't do very well. Nor would the .45 which, while noted as a good manstopper, has never been famed for penetration.
Two things, however, led to the .38 super's demise. Firstly, it had a reputation for poor accuracy. This was later found to be because it was semi-rimmed cartridge that headspaced on the rim. When gun makers changed it to headspace on the case mouth, like other, rimless cartridges did, the accuracy problem was solved. But back in the '30s, when the cartridge enjoyed its brief heyday, this had not yet been done, and the cartridge was not considered an accurate one. Secondly, the .357 magnum came along. When that happened, law enforcement officers now had the kind of power they wanted in a revolver, which they preferred to an autoloader. This pulled the rug out from under the .38 super, and it never regained its popularity (although it did, much later, find favor with competitive shooters who liked its greater magazine capacity and lower recoil in a 1911).
As for what the .357 SIG offers... simple, more power. The .357 SIG is a hotter round, that can almost equal the .357 magnum, while the .38 super, though potent, is appreciably less powerful.