In that case the 300 H&H would do fine. Sounds like the 30-06 does not have a scope on it. Does it have only open sights? The 30-06 will work fine also. This year you may want to spend the money for scope base,rings and scope for the 30-06. For deer use a 150gr. or 165gr. factory load that shoots goodin the 30-06. Natchez Shooter Supplies run specials all the time on rifle scopes. Just another thought.