Based on Larry Kelly's experience in Alaska with the 44 Mag, I would hesitate to take on grizzly or brown bears, but otherwise it's all good.
Larry Kelly was shooting 240 gr SJHP's when that griz came in his tent. No wonder they didn't penetrate! A similar weight hardcast lead would have performed just fine, and not required his friends with Rifles. Choose your boolits wisely and the 44 Mag will take you anywhere on Earth.
To answer the question...Elk/Rabbit, though the rabbit still eludes me.