Hiya Tourist, welcome aboard!
The .357 SIG, and for that matter .40 S&W, were created to put a more powerful cartridge in a firearm that would still be smaller than a full sized pistol using, say, .45 ACP. Like all good ideas, there are some tradeoffs. Both cartridges are shoehorned into 9mm Luger sized pistols. This works out OK, but it leaves little room for error as both cartridges are high pressure, unlike the forgiving .45 ACP.
The .357 SIG case is actually a bit LONGER than the .40 S&W. When you size a .40 to a .357 you end up with a neck that is even SHORTER than the factory article. I’d say 1/32 - 1/16†shorter. I found in trying to reload the SIG, it is possible and good results can be obtained but the life of the cases is only a couple of loadings. One of the difficulties is most 9mm bullets are quite tapered; I.e., there is little parallel surface to get good neck tension on the bullet. So you are subject to driving the bullet back into the case which I’ve read can escalate pressures. At any rate, it is not a good clean job like I like to do.
In terms of power, I would forget .357 Magnum and think more in terms of .38 Super, a bit more than 9mm Luger but not enough to make a dramatic difference. I have had all three and there really is nothing ot choose between them in my opinion. When you factor in price of factory ammo and availability, there is no contest that in the .355 caliber war the 9mm Luger is king. The .357 Magnum, on the other hand, in a large revolver can be stoked to be a much more authoritative cartridge than the 125 grain FBI load the .357 SIG is intended to mimic.
Again, welcome aboard and look forward to seeing some more input from ya!