Depending on how you will be hunting, either could be OK. If it will be close cover, and shots will be under 100 yards or so, both would work, but neither would be a good choice for a beanfield rifle.
Heavier weight bullets won't wear the gun faster, however it will not hit the same point of impact as lighter ones.
With proper bullet selection at the ranges the rifle is good for bullet weight probably doesn't matter, but you need to put some rounds with through the rifle and see where it hits.
The Mosin probably has a longer sight radius than the AK, so it will be easier to hit with. There are a few tricks to make a Mosin shoot better, do a search online, you may be able to tighten things up a bit.
Try putting a paper plate up at 100 yards, that is about the size of a deer vitals. If you can't hit that target every time, (or damn near every time), you may think about passing on hunting this year.