From what I've seen 100 yards is about all you can expect out of a lever gun in either caliber without aiming really high. And I wouldn't expect rifle accuracy at that range. And while a 357 can do the job, for an animal that big I'd rather have the 44.
As far as costs, I can reload a box (50 rounds) of light 44 magnum lead for around 9 bucks, or at least that was the cost before this panic set in. 38 was about 8 dollars per box of 50 lead rounds.