A 45 ACP or 45 ACP +P with a good bullet will cleanly take deer and pigs.
Of course it will, but it won't match a .44Magnum performance wise for hunting. The Redhawk gives that flexibility.
The Redhawk can't match the carry capabilities of the 1911, either, so the 1911 takes that category easily, too.
Put the .45ACP and the .44Special in identical platforms, like a double action revolver with a 3", 4", or 5" barrel, and flip a coin as to the meaningful difference. When the two different platforms are considered, the platforms make the difference.