I'm glad the poll is going in favour of the Viking, but i would point out that a poll is merely the collective opinion of people, not based on fact.
On which point i would like to explain my support for the Viking; we will start with the points that the program 'deadliest warrior' from which this topic clearly arose, presented. Firstly, the katana cannot cut through mail, this was shown in the program against stretched and taught mail, which is far less protective than it would be as hanging from the body, this fact was then conveniently ignored henceforth in the program. Also the viking would have a thick gambeson underneath the mail shirt to absorb the physical brunt of the blow as well. As for the helmet, the spartan vs ninja episode showed a ninja sword (not identical but similar construction and properties) bounce off a bronze corinthian, bronze is significantly weaker than iron, so we can also assert that the samurai would be unable to wound the head at all.
And so the first fact we can be sure of is that the samurai cannot do lethal damage to the viking. and that is without any other elements considered.
Next, the shield: in the program, they used a huge warclub thing to strike an incredibly poor example of a shield, and broke off a small section of the bottom of the shield where the bracing did not reach, and showing that the majority of the shield was unscathed, so the shield could well stand up to the weapon, then ignoring this evidence, they proceeded to claim the man's arm to be broken, which is incredibly unlikely, as the majority of the force was bled out by the shield, then there is the fact they tested against the shield, with it rigidly held by metal supports, whereas in reality the shield would be held in the arm, and the arm would bend to absorb the force, and likewise even the body itself would move with the force rather than be held like a metal frame in place to be struck.
And all this is only in the case of such a poorly made shield clearly ordered off the first and cheapest internet site available. A well made shield would perform FAR better, and as an example of this i give the experimental archaeology of http://www.hurstwic.org/history/articles/manufacturing/text/viking_shields.htm Furthermore for my own reenactment group i have also conducted my own unacademic experimental archaeology with shields made of planks.
In short even if the shield was poorly made it would still perform well enough to block any samurai weapon.
Now we come to the only point i would consider where the samurai may have some advantage, or at least that the argument has contention to it. The bow.
counter to most western myths, the samurai were first and foremost horsearchers, they only drew their katana as a secondary emergency weapon if they got caught in a melee fight. This is also the reason behind their deflective style armour, which featured easy gaps for a skilled bladesman, however from the perspective of an arrow, presents a formidable and effective defense.
As archers the samurai were trained to ride within bow range, then turn to loose a single well aimed shot at the man in the best armour, and kill someone important to gain prestige and honour.
Vikings however also had bows, basic but effective longbows, and their technique varied from loosing a cloud of arrows as fast as possible to ensure you hit some part of a large enemy formation, to the more commonly mentioned in sagas when talking of good bowmen, hiding within a shieldwall, and standing up to take carefully aimed and timed shots at the opposing shield wall's members, particularly when they open themselves up from their shields to attack.
So the two warriors have similar styles with a bow, but the samurai's great warbow has legendary range and power, and could almost certainly outrange the viking's.
So i would propose a scenario thus:
-it would be fairer to consider both warriors starting on foot, however i'll give the samurai a horse for this scenario
-the samurai would first grab his bow and begin to loose arrows before the viking could return with his own bow,
however the viking has a shield and raises it to the arrows, walking forward under the hail of arrows likely unscathed, there is a chance here that the samurai could win at this point if he gets a good shot and kills the viking before he gets close, however this is a matter of slim chance.
-now although the samurai could turn his horse and run, this would be dishonourable and he is determined to kill the viking to prove himself.
-either way the samurai would run out of arrows at some point, and the fight would progress to melee.
-the samurai still being on horseback, rides toward the viking at speed, and attempts to make a heavy cut to the viking's head, however the viking blocks with his shield (which i'll admit at this point could be weakened enough by arrows to splinter slightly, but the viking would also be favouring blocking with the iron boss of the shield more than the boards) and even if the katana gets behind the shield and strikes the helmet it will be unable to do any damage.
-meanwhile from the viking's point of view he is well protected and can aim a strike back at the horses legs, most likely with an axe or a spear. The crippled horse would topple, and either trap the rider, leaving him helpless to be finished off by the viking, or the samurai would manage to roll off without being caught, and the fight would progress to foot combat.
-now the samurai still cannot inflict any damage upon the viking, but the viking meanwhile could use the axe to hook into gaps or weak points of the armour, or even more likely, he would use the Saex, a short knife with a single edge and a viscious stabbing point, which was used when close to the enemy to make lightening fast jabs into lethal points such as the armpit, face, or gut.
-Furthermore whatever is left of his shield at this point can be used to bind the samurai's sword against his own body so he cannot attack while the viking sets about him with the saex. which would be even easier than usual seeing as the samurai would be completely un-used to shields.
In summary, the samurai would have a small opportunity to kill the viking with an arrow, but due to the shield, this would be a very slim chance indeed.
And thus is why I support the Viking.
