Prior to the introduction of the .44 Mag (yes I remember back that far) Elmer Keith stated for the non-handloader the best handgun for hunting deer size game was the .45 Colt, for the handloader it was a heavy loaded .44 Special. Either, he stated beat the .357 Mag hands down. The reason he picked the .44 Spl over the .45 Colt for the handloader was the .45's thin cylinder walls in the Colt SAA wouldn't take the higher pressures the .44 handled.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra