While I don't have a sig, my pardner has a similar situation with a Sig 229. He got the Sig 357 barrel and Sig 357 rounds. Basically, you and my pard share the same sort of setup in two different models of Sig.
Okay, with that preamble out of the way, let's talk about the round in question.
From what he tells me, the round is constructed in this way: You have a .40 cal cartridge crimped down on a 9mm slug. So the recoil or bang won't be different from a .40 cal S&W. The slug will fly at greater velocity and produce better penetration (like you'd see from a .357, but it ain't a .357 round. With me so far?
So the feel won't be different from firing a .40 cal, will send a 9mm slug down range, and achieve greater velocity and penetration. But it ain't a .357, which is why they specify that it is a Sig .357 round, not a .357 round per se.
Hope this makes some sort of sense, and that I've explained it clearly enough. It ain't easy when translating what my pardner is telling me with the T.V. blaring while he cleans his weapons! LOL!