Without that, I think the Mongols would easily win. They had a huge army that rapidly conquered the largest contiguous land empire ever. They had powerful bows, better armour, very effective tactics, but they were also excellent at sieges. Every country they conquered, they assimilated the best ideas and technology they had, which made them able to shift to very different types of warfare. They were capable of strategic maneuvering on a scale that wouldn't be seen again until WW2.

Their weakness was primarily in their rules for succession. If the death of a leader requires you to abandon all campaigns and moving all generals to the capital, after which the empire still fragments into several pieces, that's a bit a of a problem.