Well, I put a 125gr fmj 357 sig through the passenger side, and out the driver's side of an old ford pickup.I couldn't get my 9mm, .40, or .45 to do the same. IMO, enough said.
That's what we should base our ammo choice on, exact science ballistics like this
The .40 is available with more power, heavier bullets, ammo is more available and less expensive, and there are about 30 .40S&W rounds compared to less than 10 .357sig. The .40 is easier to reload.
As for power in a handgun, the recoil will be greater with a more powerful load, this is physics. If you have more power, you get more kick. Yes the .40 can kick more, or you can tone it down and kick less. I think if you get a more powerful load than a .357sig, it will be more powerful, and if you get a load less powerful than the .357sig, it will be less powerful. That was easy!!!
You can put a .357sig barrel in a .40 M&P. You can also drop in a 9mm. I don't think you can do that if you buy a .357sig.
And an important fact to remember: a 357sig IS NOT a .357 magnum. Kind of like that whole Dodge Hemi thing people get bent out of shape about.... Hemi's aren't a special engine.... The first 440 Hemi with 6 packs were, but Hemi just means the pistons had a hemispherical dome that allowed a bit more compression and directed the force a tad... The first Hemi's had some power but new Hemi's aren't anything I'd stick a badge on a vehicle about... LOL