As a Horse-archer for the Il-Khanate, there is no contest-BOWS.
Take 20 Mongol Veteran Horse-archers-park them -let them fire on infantry.
Do the same with 20 crossbows infantry.
Compare which crack more shields and make more enemy infantry groan in horrible death sounds.
The best archers you can have in the game are your Merc.Companions.Speed rules in this mod in terms of weaponry-compare the firing rate with power-bows always make the better choice.
With the exception of my 2 Medics,all my Merc.Companions have between 8-10 powerstrike and
powerdraw and only 3-4 ironflesh-most of the health points come the STR boost-so not really needed.They level fast and horse speed does not matter because they are most effective when they are not moving.They can take on 100 enemy soldiers at least,and at sieges kill at least 40 percent of defenders with their bows.I don't bother to give them shields anymore-bow,2 quivers,and a fast 1-handed weapon(Balanced or Masterwork sabres,scimitars,almogobar hatchet-speed kills most in this mod).
I recommend the Masterwork Hun Bow for a balance of range,accuracy, and speed for your Merc.Companions.The Masterwork Self-bow has more speed and accuracy but the doesn't have the range(arrow does not go straight the further the target ) but this makes it ideal for ship-to-ship battles.
The Masterwork Composite bow has accuracy and range but it is the slowest-best suited for siege battle-long distance.
The Masterwork Mongol Bow has both range and accuracy and slightly faster than the composite bow.
Remember,your archers are at their best when they are not moving.In the battlefield, park your horsearchers in front of your cavalry and your Merc. Companions beside them then watch as enemy infantry crumble in a rain of arrows.
Oh yeah,prepare to use "Hold Fire" and "Fire At Will" a lots.