This is hardly a hypothetical, the Mongols stomped everyone. They ended the Islamic Golden Age. The rivers ran red with blood, then black with ink. The filled in the thousand year old canals of Mesopotamia, leaving the land arid after the ruler of the Muslim world refused to surrender. In a fight, they could not be stopped. In terms of lasting stable government, the Romans may have better organization. But in terms of military might, strategy, tactics and ferocity the Mongols are unmatched.