I don't think it matters if the 38 Special outperforms the 38 S&W...that's not what the military was looking for at the time. If it was all about a superior cartridge, we would all just get a 500 S&W and call it a day.
According to Wiki (how correct this is, I don't know)
After the First World War, there was a move away from the larger .455 caliber. The professional core of the pre-war British Army had been decimated and replaced by a larger and mostly conscripted force. It was recognized that the short training period available to the new recruits did not give them time to become proficient with the large-bore .455 revolvers, and that a smaller caliber would be easier for new recruits to develop competence with in pistol shooting.
British Army initial specifications submitted to ammunition manufacturers for the .38/200 military loading were as follows:
Cartridge: .38 S&W (.38-200)
Bullet: (Mk I) 200 grain, lead alloy, lubricated
Muzzle Velocity: 625 FPS (+ or – 25 FPS) from 4-inch (102 mm) barrel.
Chamber Pressure: 13,000 PSI (Max.)
Webley demonstrated a lighter version of their Mk III revolver with modified .38 S&W ammunition, firing a heavy 200-grain (13 g) bullet, later known as the 380/200. It received favorable reports from the Army and the revolver was accepted in principle.
As Webley had used the .38 S&W cartridge dimensions for their revolver, and the cartridge length was fixed by the size of the cylinder of the revolver (the same as for the wider .455), Kynoch produced a cartridge with the same dimensions as the .38 S&W but with 2.8 grains (0.18 g) of "Neonite" nitrocellulose powder and a 200 grain (13.0 g) bullet. This combination gave a velocity of 630 ft/s (189 m/s) at the muzzle, and over 570 feet (170 m) per second at 50 yards (46 m). In tests performed on cadavers and live animals, it was found that the lead bullet, being overly long and heavy for its calibre, become unstable after penetrating the target, somewhat increasing target effect. The relatively low velocity allowed all of the energy of the cartridge to be spent inside the human target, rather than penetrating completely. This was deemed satisfactory and the design for the .38/200 cartridge was accepted as the "380/200 Cartridge, Revolver Mk I".
