Rimmed centerfire autoloaders need special design attention.
I've got an early S&W Model 52 that runs .38 Special hollow-base wadcutters only. That particular round is an absolute bitch to chamber in an autoloader, because it resembles nothing more than a fired .38 Special case, since the bullet is seated flush with the case mouth. But they chamber and autoload just fine in the old Smith bullseye gun. How'd they do it? A very gradual feed ramp, polished smooth, and a magazine design that won't allow the rims of the top rounds to get behind the rims of the rounds lower in the magazines.
Same goes for my .357 Desert Eagle. (And no, it hasn't jammed on me, Villain, the company is still in business) The M-16 style bolt face of the big gas autopistol has no problem with the rimmed rounds. The magazines don't have problems, either. Not a good concealed-carry gun, though.
The Coonan, especially the shorter Cadet model, is about as small as one wants to get in a .357 Magnum autoloader. I seriously doubt a .357 Sig could hold a candle to it, especially when you run stuff heavier than the Sig's much-vaunted 125gr bullets.