Either one will do the job. The 45 Colt will do everything the 44 Mag will do but with less pressure because the case is bigger. By the time you get past the 44 Mag in power with the 45 Colt it's not much fun to shoot.
Either one launching a 250 or heavier bullet at 1200 fps or faster will take anything on earth, with good bullet selection, that being the key. Good bullet selection is code talk for hard cast solid with as large of a meplat as you can find. I like them both. It's really preference since they both will do what you need them to do.
The 44 Mag is cheaper to load for and components are more available.