Vikings did actually use bows to soften up opponents before engaging in open battle, tho they considered it a less honourable way to kill an enemy than hand to hand combat. Add in shields to the Viking side and they would have the advantage in a war especially considering the two handed axes that can cut through bone and plate armour in kind. The Samurai sword on the other hand is designed for slicing and is not ideal for combating chain armour.
One on one the samurai may have an advantage if the battle started at a long distance where he would have time to fire of multiple shots before the charging Viking reached him but assuming the one on one fight is a duel and they start in close proximity the bow becomes useless and the advantage goes to the blocking power of the shield and the crushing power of the axe and Viking sword both of which are adapt at combating even full plate armour.
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