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.
Yep. They are both fine cartridges, and each has small advantages over the other. If you want a single-action revolver, get a .45. If you want double-action, get a .44. If you are dead-set against reloading, get a .44. In a rifle, the choice probably comes down to something like the twist rate.