I also feel archers are underpowered in MTW, though only vs lightly armoured and unarmoured units. Vs armoured units they are realistically less effective. The Samurai Archers in STW always seemed to do a lot more damage to me. I often find that during battle I can find a good vantage point for my archers but rarely feel that they've done enough damage when their quivers are empty. I also feel that the AI archers are less than effective unless they're in ridiculous numbers. I can usually charge them down with light cavalry and take only a few losses from the volleys they let off. In reality cavalry charging straight at a unit of archers would take many more losses before closing with them, unless they were suitably well armoured.

Perhaps lethality could be increased slightly and the armour piercing decreased a bit?

Horse archers are worse. I have no idea why their "mounted longbow" has worse accuracy than the shortbow, when throughout history horse archers were some of the best archers ever. Also in this game they can only fire when stationary so it's not as if the lack of accuracy can be put down to them being on the move.

This shouldn't be a problem for much longer however, as I intend to equip them with the compound bow. The question is though, should they use the same compound bow as foot units (such as JI, Futuwwas, [Eastern] Archers and Psiloi use) or should a less accurate version be made for horse archers (though I can't see the sense in this)?

Another issue is, which horse archer units should use the compound bow? All or only certain units?

With the horse archers previous bow out of use, we have a free weapon. I remember someone mentioning differences between the mongol bow and the eastern compound bow? If this is the case the old mounted longbow slot could be used for this, as a mongol bow. I am no expert on this though and would need some info on the differences between the two.