I personally prefer the 45 Colt, especially with 250-300 gr. hardcast bullets, however if you need ammo and you don't have any, it is very difficult to find good 45 Colt loads in many smaller towns and remote locations. That may cause me to lean towards the 44 in some applications.
The 44 mag seems to available in loads that will suffice almost everywhere. I prefer the heavy loads for both calibers in my Blackhawks, but I do not like them in most DA revolvers I have fired.
Either caliber will do the job on most game in the lower 48 states. I personally have taken two elk with a 44 mag and several mule deer. I have also taken one moose, several deer, a couple of antelope, a black bear and a large mountain lion with a 45 Colt. I would guarantee none of these animals knew the difference between the 44 and the 45.
My only experience with a Wyoming Grizzly was when we both agreed to go in opposite directions. I have no idea if either caliber would have done the job. If I had been carrying my 44 mag rifle I would have felt more comfortable because of the extra horse power a rifle gives, but I don't go into that country any longer without my heavy rifle and my handgun.
