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What is "magnum" speed? Is there any real difference between a 30-06 at 250 yards or your Norma at 350?
At what range do you expect to see animals? If they are likely to be within 200 yards then go to a heavy controled expansion bullet. Once you get out beyond 250 yards flat trajectory and accuracy are of more concern. If you may encounter animals from "in your face" distance to the far side of 400 yards then a bullet like the Accubond, Interbond, or TSX may be good choices.
As for weight ............. there is so little difference in performance between the 165 and the 180 that you should just go with whichever weight your rifle prefers.