Sigh...
The idea that the the .357 Magnum is a better one-shot stopper than the .44 Magnum comes from the work of Evan Marshall and Ed Sanow, two former law enforcement officers. Their original book "Handgun Stopping Power" attempted to rate the effectiveness of various handgun rounds/loadings based on actual real world shootings. I don't want to get into it too much here, but let me say that Marhall and Sanow's work has been widely criticized for the authors' apparent complete lack of understanding of statisical and scientific analysis principles. Anyone with even an indroductory education in statistics and scientific methodolgy will immediately see the flaws in their methods.
That being said, the .357 Magnum MAY be a better manstopper than the .44 Magnum, even though the .44 mag has nearly twice the muzzle energy (roughlly 900 ft.-lbs. vs. 500 ft.-lbs.) and much greater weight and cross sectional area. Here's why: overpenetration. The .357 mag, with good hollowpoint bullets, may deposit all of it's 500 ft.-lbs. or so of energy INSIDE the target's body. The .44 mag, with it's heavier bullet, may zip right thru a body before fully expanding, expelling most of it's 900 ft.-lbs. or so down range of the target.
Room for debate certainly exists. Much is changed by differences in powder types/charges and bullets weights/designs. When it comes to stopping power, it's not all about energy.
One last thing: barrel length certainly can affect muzzle velocity. To achieve maximum velocity from a particular load, all the powder must be burned at the exact instant the bullet leaves the barrell. Any shorter, and powder is still burning in the air, just creating more muzzle flash, while the bullet is long gone. Any longer, and the bullet slows down in the barrel due to friction. The type of powder and it's burning speed affects this greatly. Going by memory. a typical 125-grain .357 load gets about 1100 feet-per-second out of a 6-inch barrel. The same load in an 18.5" carbine barrel will go about 1800 fps, result in a huge gain in energy, beacuse energy is mass times velocity squared.
Not all rounds behave the same. The 9mm parabellum, for example, only gains around 100 fps by going from a pistol length barrel to a carbine.
Me? I usually carry a .38 special snubbie. Sometimes a .357 mag SP101.
Valar Morghulis.