A .357 magnum will hit harder and an efficient JHP will more than enough to prevent overpenetration. I use Remington 125 grain JHP 1450 feet per second, 583 ft/lbs of energy as my home load. I shoot it at the range, so its quite familiar with me. When fired, it does announce "I am a .357 Magnum!"
Downside, a snubnose will be punishing on the shooter, and the powder will not be finished burning by the time the bullet leaves the barrel therefore creating terrific muzzleflash.
Upside: Compatible with .38 special, .38 Special +p, and .38 Special +p+. .357 magnum loads come in a wide variety of power levels from a tame Golden Saber to Buffalo Bore's finest beast killer. 10 out of 10 bad guys hate this round.
.44 Special offers better cross sectional density and is slightly slower than .357 magnum ammo. It is very close to .45 ACP loads.
Downside: sparse ammo, and the ammo found is typically quite expensive.
Upside: Dirty Harry would be proud. .44 Magnum can be also used in a snubby that isn't strictly .44 special. 10 out of 10 bad guys hate this round.
Verdict: Either will do damage without tactical liability with practice and a calm disposition when the moment of truth is at hand. Carry with confidence!