The .44 mag is just a super cartridge for all around hunting in North America. Lots of variety in component selection, superb accuracy available at all power levels, great selection of arms to suit the individual and the power of the cartridge is manageable by most dedicated enthusiasts.
I adore the .357 magnum in a nice 6" DA revolver; pretty to look at, does a good number of things quite well but its not going to match the versatility and efficacy of the .44 in the hunting fields. I love my 6" GP100 and carry it often in the field when I'm not hunting. Great solution for varmints of both the biped and quadriped persuasion. And just fun to shoot, period. When I go out after deer the 5.5" Super Blackhawk in .44 gets the nod. I've shot muleys with both cartridges and the .44 is noticeably more effective at any range.
If you're after a hand gun that will be primarily a hunter then go with the .44.... and add the .357 later when the budget allows. A feller probably ought to own a good hand gun in both these excellent cartridges.