I think the 44 is a better choice in a rifle. Ammo costs and availibility is so close it is a non-factor, about $1 more for 20 rounds of 44 over 357 for plinking ammo. And 44 is more readily available, especially in heavier weights suitable for hunting. Most 357 ammo on shelves is 125 gr SD loads.
The best 357 loads won't quite equal 30-30 ballistics, and only at ranges up to 50-75 yards. Hot loaded 44 mag ammo gives up nothing to a 444 at close ranges. Lower powered loads are good for plinking and smaller game. 44 shotshells hold enough shot to be far more effective than 357 increasing versatility.