Zhu Xi has no access to regular archers, which is what you want against longbows. Zhuge Nu are not effective against them, so they can't fight Byzantine longbows in feudal age.
Enough Cataphracts should beat the lancers even with the Dali Horses attack speed upgrade, as long as they are backed up by longbows.
Zhu Xi does not have the Imperial Academy, so killing an Imperial Official is a full economic kill. They cannot easily reproduce it like the Chinese can.
Byzantine Royal Cannons are superior to Zhu Xi's bombards: three can one-shot a Nest of Bees, and they have more range.
Zhu Xi and China often have an inflated score due to additional landmarks, so don't trust the score when facing them.
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