There is a lot of discussion about the 44 mag vs 45 colt. Some of It rather heated.
On top of that, there are multiple parts to the answer.
45 colt is deadly. Lots of animals shot with it. Most factory loading are loaded to be compatible with the "historic" single action colts and colt clones and are rather weak for hunting, but at close range and with proper placement are very deadly.

A +p (stronger then normal loading) 45 colt will do deer and hogs with no problem. I would assume elk would be fine with proper range and placement too. These stronger loads must only be used in guns that are designed and built for the higher pressures. The Blackhawk Bisley you shot is one of such guns and will shoot the stronger loads. Select manufacturers make such +p loads and typically you must buy them online or by phone and have them shipped vs buying 44mag off he shelf in most gun stores. Alternately, load your own.
This is just a quick answer and others here know tons more.