All the evidence I have seen, that is, reports by people who have shot reasonable numbers of people with both, shows that 9mm ball and .45ACP ball have indestinguishable effectiveness. Strangely enough, that fits well with the oh so often repeated stuff about all pistol rounds are feeble and only use a pistol to fight your way back to your rifle and so on. I think we can assume that the same just about holds true for hollow points in both.
What this means is that the extra diameter and mass (and even some KE) of the .45ACP is compensated for by the extra speed of the 9mm. This suggests that, given the right bullet design and mass, we could find some speed for a .22 which would be just about equivalent to the 9mm and .45ACP as well. Equally, if the .38 Super, bullet mass for bullet mass, is a faster 9mm then we should expect its terminal performance to be better than the 9mm. People who use it for hunting report precisely that! Since the 357SIG is slightly faster again, we should expect it to be slightly better again. As sigcalcatrant says, the 357SIG certainly produces a far more impressive wound than the 9mm and it is hard to imagine that such a result does not also prove to be more effective.
As a side issue, various people have talked about the appearance of wounds created by 9, 40, 357 and 45 as being indistinguishable. This is true of an entry wound for simple reasons. The ballistic pressure wave which forces tissue out of the path of the bullet (this is nothing to do with the remote effects on the brain of such waves and is simple physics) pushes tissue mainly ahead and forwards of the bullet. Only a very high velocity, high energy, bullet which expends most of its energy in the first inch or two, like a varmint rifle bullet, will create enough pressure to force tissue to explode backwards in the vicinity of the entry hole. Because of this all that appears on the outside is a smaller than caliber diameter hole in the skin as the skin is flexible and stretches round the bullet to some extent. To see the actual damage done by a bullet it is necessary to transect the bullet track and look at the damage done to tissue to either side of the track. This is not feasible with a living patient.
Even with the wound transected in this way the 9mm and .45ACP show very similar injury characteristics because bullets do not just make a simple caliber or expanded diameter hole. As sigcalcatrant says, the difference of the 357SIG is clear and significant.