The evidence that the .22 Magnum is more effective than the .38 Special 158 grain RN are tests conducted with ballistic gelatin by IIRC the Secret Service in the early 70's plus my observations in tissue destruction in turkeys, various varmints, and deer over a 40 year+ period of using the .22 Magnum
In ballistic gellatin, the .38 Special 158 grain round nose produces limited cavitation, While the .22 Magnum with a strong jacketed soft point produces cavitation that exceeds the .38 Special 158 grain Round Nose considerably.
Regretably, the data I had on these tests, as well as most of my firearms and ammunition library, was destroyed by Hurricane Hugo fn 1989.
Winchester and CCI have recently developed .22 Magnum loadings for optimum performance in short barrels that, based on the information I have read, will prove to be more effective than the .38 Special loading that for years was the standard police cartridge in most metropolitan areas.
The .38 Special 158 grain Round Nose produces 200 to 225 foot pounds of muzzle energy while several loadings of the .22 Magnum with bullet weights ranging from 34 to 50 grains produce muzzle energies ranging form 240 to 338 foot pounds (Ammo Encyclopedia by Michael Bussard).