In the right hands, you probably wouldn't see much difference in terminal performance between the two calibers. Since you don't handload, I say go with the 44. That said, there are some good 45 Colt +P factory loads out there if you're willing to shop around online. May not be as cheap, but they're still good.

I think Whitworth has proven the 45 is capable of taking down deer at the very least.