Both are fine for deer.
Remember, most states don't allow ball ammo for hunting. All surplus will be ball ammo.
Look for Wolf, S&B, Privi Partisan or Igman for ammo for both calibers. Try Centerfire Systems and AIM Surplus.
The issue sights may not adjust enough for the hunting loads, requiring some mods to the front sight height.
The Yugo Mausers are usually good shooters.
In the Mosin Nagants you can find good shooters in many of the models. The Finnish models are very good shooters in general.