In today's world of magnumitus, it seems that if you can't shoot a ball of flames out 3' and launch 400grs of Rockwell 40 lead at some ridiculous warp velocity, you can't even punch a hole in Bugs Bunny.
The truth of the matter is, when you get to bullet weights in the 240-280gr range, they don't have to be launched nearly as fast as their lighter counterparts to get the same or even better results. Weight will usually trump velocity most days and in most cases with handguns.
I have been extensively testing cast bullets through calibers ranging from .38 SPL up to 454, and I can tell you for sure and certain that a 950'ish FPS 250-270gr .452 RFN bullet of even a 10 BHN will penetrate up to or more so than something moving 3-400fps faster, everything else being equal.
With the Colt, I have a 7.5" Redhawk, and being I am in the position to do so I HAVE worked it up into the loads worthy of matching the 44. You don't need that, not unless your looking to go find a record Bison or Kodiak bear. There isn't much wondering around in the lower 48 that the mundane 850 - 950fps loads using a 250-270gr cast bullet won't take out IF you put the shot through the boiler works. At 50yds if you do your part you will have meat in the freezer.
This isn't meant to diss the .357, as I love that caliber too, but in the past 3 years I have grown just as, if not more fond of my 45 Colt than my 357, 41, or 44 magnums. I would have thrown my 454 into that, but where the Colt leaves off, it picks up, and there is something to say about a 300gr WFN rocking out at 15-1600+fps when it impacts something like a 200gr feral hog. But thats not what we're talking about here.
Of the two mentioned, consider this, handloading will give you the best options for either. The key thing for me would be if you wanted to pay $30-40 per 20 for a decent box of hunting loads for either and only get 20rds. Remember, practice is paramount with handgun hunting, just as it would be with a SD type training. You will need to put a high number of rounds downrange using what your going to hunt with. Trigger time with a .22 simply isn't comparable to shooting THE load you WILL be hunting with. All shooting with a .22 does for you is make you more accurate with the .22, it does nothing to give you the recoil, or blast, or help you to learn the trajectory or grouping of your hunting loads in field conditions at ranges you intend to hunt.
The 45 Colt with a good load in the 950fps range is not hard to shoot, but it does have to be shot in order to be proficient with just like anything else. Regardless of which one you choose, I would first consider how your going to feed it, and with what, to get to a level of confidence and accuracy that will allow you to put the bullet where it needs to be each and every time.