Both 44Mag and 45LC (with some 45LC+P fodder by Cor-Bon, Buffalo Bore or similar) can do the same jobs. The 45LC+P can get there with a bit less peak pressure but the differences are really marginal.
Out to 100 yards, either caliber from a rifle can hunt black bear, elk or the like.
There are "Cowboy Loads" for either caliber, consisting of lead round nose fodder doing less than 800fps from a handgun. These can be very accurate and are extremely mild to shoot, and would be perfect for rabbit or similar without screwing up the meat too badly.
There's also "personal defense loads" for either, usually a 200grain JHP at around 1,000fps. These can handle deer or coyote, and of course the dreaded two-legged rattlesnake
. But if you're in black bear country you'll want "hot hardcast" in the handgun, which will perform adequately in a personal defense role regardless of target.
Which would I pick? I'd try and match the rifle, myself. The Ruger 44Mag clip-fed levergun handles well and has a sweet short leverstroke. *Somebody* out there is making 10rd mags for 'em, although I haven't been able to find 'em yet 'cept for one guy in *England*
. Marlin leverguns in either caliber are guaranteed able to handle any load that'll work in a Ruger SA.