First--what do worry most about attacking you?
WILDCHILD,
I would think the first question is what is the greatest threat? Cougars are not very large, about the size of a large dog. Either round would work fine.
Elk and Moose are rarely recorded in attacks on human as far a I know. If they do attack, the .45 Long Colt is the better of two bad choices. Neither is big enough for hunting these animals, so they may or may not do the job.
When it comes to Bears, the question is black or brown. Black bears do not get all that large in most of the U.S. I have heard of really large (read about 600 pounds) up in Canada. Even so, a 400 pound bear is still within the capability of a .45ACP with good ammo.
Brown bears are different. They are huge and either round is underpowered to fend of a large bear. They can easily get to half a ton.
When I lived up in Canada, where there was a good chance of running into a grizzly, the local farmers carried pistol grip, pump action shotguns of the MOSSBERG cruiser type. Why, because a 12 slug leaves ANY .45ACP or .45 Long Colt load in the dust.
If your primary threat is of the human kind, then the .45ACP is the hands down favorite. It is controllable, quicker to reload, has a higher magazine capacity and will usually be lighter to carry.
If you are going to carry for self defense against people, forget about reloads, it is just one more potential legal problem if you actually have to defend yourself.
Good luck,
Jim