Personally, I'd pick the 44mag all day over a 10mm. I hunt with a S&W 629 Classic with 8 3/8" barrel, carrying in a shoulder holster. I carry this revolver, and also carry my rifle for longer shots considering I have not scoped the 44mag.
I will add that the Ruger Blackhawk hunter mentioned earlier is also a great 44mag that will function very well in the field. I hope to add one to my collection before too long.
Whichever revolver you choose, if you plan to keep it I would recommend you get a trigger job done on it because that will obviously help you to make better shots.
God bless.
CR