I agree that the .357 would be a great choice, but if limited to your original two choices, even though I have and love a 4 5/8" .44 Spl. Ruger Flat Top Blackhawk, for general "woods loafing", as it is called, I use a 4" S&W Model 10 .38 Spl. It will handle anything I am likely to run into around here. Although its not on anybody's list as a deer hunting gun, I am confident that if it was necessary to shoot a deer with it, I would come home with venison without much of a problem. I am also confident that if I had to use it in a contest against a wolf or black bear, I would win.
When I take it out west on a prairie dog shoot, I also keep a couple of CCI shot loads in it.
To my knowledge, there are no commercial shot loads in .44 Spl. (they do make them in .44 Magnum, though).
My K-Frame .38 is lighter than my .44 Spl. and I find it easier to carry. It is also much faster to handle and quicker to reload.
But, use the one you like the best.