The only use I have for a .44 magnum is a short, handy, carry-anywhere carbine for "bear repellent" while at our remote bush camp. It's the absolute minimum I'd consider for grizzly bear, but the .44's advantage is the small. light, handy Rossi 16" barrel / Stainless steel carbine that it's chambered in. It is handy enough that I can actually take it with me nearly anywhere. My bigger marlin Guide Gun 45-70 mostly stayed in the cabin of truck because it wasn't nearly as handy. I have not had to kill a bear with the .44 yet, but it has been a comfort in my hands during several close encounters with mischievous black bears. A bigger rifle back in the cabin would not have been so encouraging.
If actually hunting with a .44, deer / black bear at less than 100 yards would seem a reasonable limit. I have much better cartridges to choose from for moose or elk or other larger game.