Since you didn't give a purpose, I'm going to assume general purpose, versatility.
.357 mag because it shoots flatter, faster, and more energy than .44 spl also higher sectional density loads, available for the .357 mag gives it an advantage on thick skinned/heavier game. And generally a larger bullet selection is available for the .357
The .44spl is basically, ballistically, a glorified .45acp in a revolver cartridge. Ok so it's .43 caliber, not .45, but it's close enough, and a 200 grain .44spl load typically leaves a 4'' barrel at roughly 870fps. Compare that to .45 acp the military load 850fps with a 230 grain bullet. Really, not much difference, IMO I doubt you'd see much, if any, difference on game or in a SD situation.
If it were .44mag versus .357 mag there'd be a more even comparison but the .44 special, really doesn't seem that 'special' to me. .357 mag has a clear advantage in almost every category, IMO.