I don't have the .44, but this question comes up a lot and I always take a peek to see what is said.
Based on reading, seems like some of the bigger differences are felt recoil, reloadability, and maybe to an extent factory ammo price (I don't really know what .44 goes for nowadays). If it were me, I'd focus on those aspects. I've always been a fan of the "companion revolver" deal too, so personally I factor that in. +1 for .44 mag on that.
For a lot of the other stuff, it sounds like they are about equally good at. Or too close to call. Just my humble thoughts, which I readily defer to hunters who have actually used both.