I don't own a .357 Magnum and know relatively little about the caliber, but I know that the .357 SIG auto round was designed to emulate the 125-grain .357 Magnum loads like the Federal 357B 125-grain. It seems that if the 158 grain loads had more potential, the round would have been built around it instead.
The 357 Magnum was introduced in the 1930s. The standard weight bullet for it when introduced was a 158 gr. load, the same as for the 38 Spl. The round soon gained an wide following as a hunting, sporting and self defense round and a variety of bullet weights and styles were developed for it. But it was around the 158 gr. load that it's reputation was built.
In the mid 1970s a small company called Super-Vel headed up by Lee Jurras developed a line of lighter than average weight hi-velocity jhp bullets for a number of handgun calibers. For the .357 Magnum they introduced a 110 and a 125 gr. jhp at close to 1400 fps from a 4" barrel. With their hollowpoint bullet and at those speeds the bullet expanded more reliably than previous efforts at hollowpoints. The round developed a good reputation and other manufacturers followed Super-Vels example. The 125 grain loads enhanced the reputation of the .357 Magnum which was already impressive. Over the years bullet development enabled other loads to expand more reliably as well. 158 gr. hunting and self defense loads that reliably expand are currently available. Heavier loads are also available for hunting.
In the 1990s two gun writers and former cops published a series of articles and books claiming that certain bullets made by particular companies in the 125 gr. load for the 357 Magnum had a better "One Shot Stop" percentage than some other bullets by different manufacturers and some in other calibers. Though in many cases they maintained some bullets in different calibers outperformed the .357 in some 125 gr. loads.
So the work of Super-Vel and some years later the articles of Marshall and Sanow are the source for the "more reliable" rep of the 125 gr. loads.
The .357 Sig round is based on a necked down 40 S&W case and was introduced in 1994 a few years after the 40 appeared. Because of the length of the necked down case the 125 gr. bullets perform better from it than 158 gr. loads. So do 115 gr. loads which produce very impressive velocities. Though it seems 147 gr. loads do fairly good as well. The round was named the .357 Sig because Sig developed it and to piggy back on the popularity of the .357 Magnum.