Tough question, Alan. I think the .357 Magnum's wonderful reputation as a "stopper" is largely with one bullet weight, namely the 125gr. JHP. This seems to strike the perfect balance between velocity, impact, expansion, etc. With other loads - e.g. the 158gr. JHP - the .357 does not have quite as good a stopping record. I don't know about the very light-for-caliber 110gr. rounds - certainly they're not as lauded as the 125gr. stuff, and I would think that they would lack sufficient penetration for certain tactical situations.
The .45 ACP had a good reputation in the days of ball ammunition - a solid .357 slug is not going to do as much damage as a solid .451 slug in terms of permanent wound cavity, and with solids, the temporary cavity is nothing to write home about. With JHP's, the .45 improved substantially, into the 19-out-of-20 range with some rounds: but the .357 improved even more with the 125gr. round, ending up marginally ahead of the .45 by M&S's take on the subject. The added velocity and expansion of the .357 allowed it to equal the lesser expansion and lower velocity of the .45 in its effect on human flesh.
The 357 SIG was designed to duplicate the 125gr. .357 Magnum load, and did so very well, coming within 100 fps or so from comparable barrel lengths. Its street results so far have been pretty good, judging from feedback provided by the Texas DPS, the Secret Service, etc. Both of these rounds are very flat-shooting, and are said to have a "hit-by-a-lightning-bolt" effect on someone shot with them. The .45 does not have the same dramatic impact effect (probably due to its lower velocity in standard loads), but seems to drop an aggressive attacker just about as well, given a good COM hit or two (or three). The really light, fast .45 loads (e.g. the Cor-Bon 165gr. and 185gr. JHP +P's, and recently the 165gr. Pow'rBall) are said to deliver much more impact shock, with visibly greater reactions in those shot with them, but I can't quote first-hand accounts. Makes sense, though, as these bullets are moving at about 200 fps faster than standard .45 velocities.
I guess that velocity does count in the "immediate-effect" department, but this is still a hotly-debated issue, and I don't think we're likely to find general agreement on it during our lifetimes.