The .357 Sig comes reasonably close to duplicating the ballistics of older 125gr .357 Magnum loadings, but that's about where the similarities end. To understand the similarities and differences, you really have to understand the history of the .357 Sig cartridge.
During the 1970's and 1980's, 125gr SJHP .357 Magnum loadings (particularly those from Remington and Federal) gained a fearsome reputation for effectiveness when used against erect bipeds. Nearly all the police departments that used these loadings were quite happy with them until semi-automatic came into vogue for police in the 80's. At that time, the two main cartridges used for police semi-autos were 9mm and .45 ACP as neither .40 S&W nor .357 Sig had been invented yet (10mm was around, but it never really gained a huge following). Between the two, 9mm was far and away the more popular because it gave the most significant capacity advantage and capacity was the primary reason for switching to semi-autos in the first place.
The problem was, and to some degree still is, that you simply cannot make a semi-jacketed bullet completely reliable in a semi-automatic handgun. JHP bullets of the 80's and early 90's were, by today's standards, fairly primitive and, with 9mm in particular, you either had to go lighter and faster at the expense of shallow penetration or heavier and slower at the expense of aggressive and reliable expansion. This had never been an issue with the .357 Magnum because SJHP bullets expanded much easier than JHP's of the time and because the .357 Magnum could drive a bullet of a given weight much faster than a 9mm could.
It was then decided that if the same weight bullet could be driven at the same velocity of the 125gr .357 Magnum loadings in a more semi-auto friendly package, that the effectiveness of the Magnum could be successfully transitioned to a semi-auto platform. Unfortunately, it was an idea that worked much better in theory than in practice.
Early .357 Sig loadings did indeed live up to the Magnum's ballistics (125gr bullet at 1450fps), but they did not use the same types of bullets. Early .357 Sig loadings used standard 9mm bullets which were designed to be driven at 1000-1200fps. When driven 200-250fps beyond their designed velocity window, these bullets would frequently overexpand and/or fragment resulting in relatively shallow penetration. The cure for this issue was two-fold: first, most manufacturers dropped their velocity by about 100fps to approximately 1350fps. While at the upper limit of velocity, many 9mm bullets could still hold together well enough to penetrate adequately at 1350fps. The other solution was the the bullet makers designed newer, tougher bullets better suited to higher velocity than the older 9mm bullets were.
That brings us to the .357 Sig loadings of today: most run a 125gr bullet at approximately 1350fps with expansion and penetration similar to that of the newer premium 9mm and .40 S&W loadings. While that is certainly good performance, it is not the same as what a .357 Magnum is capable of.
The most obvious difference is the range of bullet weights available. Very few .357 Sig loadings exist with bullets heavier than 125gr and the few that do cannot come close to matching the velocity attainable from 140gr+ .357 Magnum loadings. Also, while 1450fps was the approximate velocity of older 125gr .357 Magnum loads, it is nowhere near the top end of velocity for that bullet weight in that cartridge. Boutique ammunition makers like Buffalo Bore, Double Tap, and Grizzly have produced 125gr .357 Magnum loadings that can crack 1600fps from a 4" barrel and even more from a longer tube. I know of no maker with a .357 Sig loading faster than 1500fps from a common semi-auto.
Bullet construction makes a big difference too. When loaded with modern bullets like a Speer Gold Dot or Hornady XTP, a 125gr .357 Magnum is capable of much deeper penetration than a .357 Sig is. Brass Fetcher did a test of a .357 Magnum 125gr Speer Gold Dot which went through over 16" of ballistic gelatin, most .357 Sig loadings run in the 12-14" range. Finally, the old SJHP bullets do not perform like JHP semi-auto bullets do. While penetration was reasonably similar to modern JHP's (11-13"), the expansion characteristics are very different. The SJHP, when driven at high velocity, routinely shed their jackets in large shards at 6-10" with the lead core still penetrating 11-13" while most JHP's designed for semi-autos tend to either fragment very little to none or fragment very quickly with total penetration of less than 10" (6-8" is fairly common).
.357 Sig is certainly a more than capable self-defense cartridge, but it cannot duplicate the .357 Magnum beyond paper ballistics due to the constraints of its design and the platform for which it was designed.