The main reason I'm going with a .44 mag over the .357 is in my opinion the .44 mag has better stopping power for defense against dangerous wildlife.
For hunting medium to large game and defense against such animals, I'll opt for a .44 mag heavy cast bullet. For defense against humans, I'd probably load it with .44 special rounds. For hunting small game like rabbits, squirrels and such, I prefer to trap or snare those anyway. But if I had to tangle with an angry brown bear in the woods, short of a magnum rifle round, I'd rather have the .44 mag over a .357 mag. Again, JMHO.
(If it was only one gun for defense against people only, I'd probably go with a G-19. But only one handgun to do everything including hunting, for the rest of my life, is why I went with a revolver in the big bore 44.)