The truth is that there is virtually no difference between the two. Yes, the 45 slug is larger and heavier, but that means the 44 has a better sectional density for the same weight bullet. Yes, weight for weight, the 44 can be fired at a higher velocity, but at the expense of extra pressure. Every comparison between these great cartridges is a trade off with a different comparison. And all the differences are so slight that they are virtually meaningless in their effect on game.
I prefer the S&W Model 629 to any other commonly available and affordable revolver in the two calibers, so I shoot the 44 mag more often. But I also have a Ruger Bisley Blackhawk in 45 Colt. Here is a numbers comparison for you between max loads with equivalent SDs:
