Actually mounted xbows are better in the archer duel than any HA, so once westerns have mounted xbows the byzantines are outclassed in all department. Not to mention guns, musketeers and pikemen ...

Just because the AI cannot handle any of these troops (and thus the player will never or rarely ancounter them and even those time the AI will mess it up) it does not mean that the byz army is at the same level as the armies of western factions because it is not.