I don't believe that statement is entirely accurate.To answer your question, gunpowder burn rates, though they do vary, all burn blindingly fast. Rest assured that all of it is burned by the time that slug starts moving down the barrel -- doesn't matter if it's a .22 or a .50cal.
Now when you get into terminal ballistics between .38 vs .357, you'll find that the .357 has a better "one shot stop" street record, specifically with the .357 Magnum. I'm going to try and avoid starting a caliber war here, but to sum it up, the .357Mag is more powerful than a .38. That's not to say that the .38 is weak. Many people load up their .357 magnums with .38+p ammo for easier recoil control and less muzzle flash. .38Special ammunition is ballistically very similar to 9mm Luger ammunition, if that means anything to you.
A .357 slug coming out of a snubbie is ballistically more lethal than a .38 slug coming out of a snubbie, but either one will kill. Just pick the one you can handle best.