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Wow I have to disagree with cycwynne above. The Mongols ruled China for more than a century, the Yuan dynasty 1279 -1368, though they had made major conquests in China in the mid 1200s. Mongols rulers such as Kublai Khan became VERY civilized with an organized empire. The Vikings did not "convert" to Normans (though I'll grant that they did learn to speak medieval French). They had always been "Normans" - which means Norsemen or men from the north. Also the major climatic change, the "Mini Ice Age in Europe," did not begin until the early 1300s - - long after the Norsemen had settled down in their new lands and become Christians. [They could not pillage easy targets like undefended monasteries with a completely clear conscience after they became Christians in the late 900s.]
Similarities: Both seemed to be an unstoppable military force, though both were checked in spots. The Anglo-Saxon (essentially German/English king) Alfred the Great kept them from completely occupying England - though the "Normans" would indeed complete the conquest of England after 1066 AD - and the Normans were transplanted "northmen" or "Vikings" who had settled in France after ~ 911 AD.
The Mongols were stopped twice by the Vietnamese (tough people). They were also checked by the Japanese twice in the late 1200s, though storms at sea helped on both occasions. I think the Mamelukes also beat the Mongols in the Middle East after the Mongols had already taken Baghdad (late 1200s).
Differences may be more striking. The Mongols were an "en masse" hoard - while the vikings usually attacked in smaller groups. Both were very mobile, but the Mongols were horsemen of the plains or steppes while the Norsemen were seafarers. Mongols used cavalry mobility and archers while the Vikings fought on foot with hand held edged weapons.
Good question though.