Way back when I shipped to AK, I traded my .357 Mag Blackhawk for a .41 Mag BH. My hunting buddy carried a .44 BH. Shooting and comparing both, I preferred my .41 to the .44.
I handloaded Speer jacketed SWCs (using Blue Dot at the time) and during un-scientific testing found that my .41 put holes thru the same Birch trees his .44 did, and with less recoil.
True, the .44 has more potential--if one reloads to its full potential--but for the average shooter I feel the accuracy and controlability of the .41 out weighs the .44's benefits. If you really need more power, then jump to the .454 Casal, the .460, or the .500 magnum.
In all practice, a deer or any other medium-sized game isn't going to know the difference in which hit it. If you're only going to shoot commercial rounds, I'd say go with the .44 only for ammo availability sake. If reloading, I'd opt for the .41. Run a box of hot loads thru both and you'll understand why.