Anyone who has ever played an RTS knows that horse archers offer a great combination of firepower and mobility that is very difficult to counter. Ghengis Khan's Mongol hordes proved this in real life when they carved out a vast empire in the 12th and 13th centuries. The Romans however relied more on the strength of their footsoldiers armed with Pila and short sword when they carved out their own vast empire more than a thousand years before. So who what would have happened if these two great forces clashed across the span of time. Who would win a war between Mongol Horde and Roman Empire at the height of its power?
Personally I vote for the Romans to win the war although I could see the Mongols winning the first battles. The Mongols were superb tacticians and the mobility of the horde would prove difficult to counter. The composite bows of the Mongols could be effective against Roman armour. In the long run though Rome was not just about the prowess of individual armies it was about a whole economic and political system that could lose battles and still win wars. The Carthaginians, the Gauls and the Germans all managed to defeat Roman armies but eventually succumbed to the might of Rome. Of course the Khan Empire was also based on excellent administration and a self sustaining system of growth. The Mongols also managed to turn around defeats but the Khan's reliance on highly skilled horse archers was both a strength and a weakness. Mongol horse archers were born in the saddle and learned their superb horsemanship and archery skills as they grew up. They could not be replaced quickly. The post Marius Roman army on the other hand could turn just about anybody into a top quality soldier in an almost industrial process. I think that once they had woken up to the danger of the Horde the Romans would have been able to match them tactically and outpace them in the production of replacement forces.