With archers and horse archers you can hold alt while clicking to attack while they still have arrows. (While holding alt the mouse icon will change from a bow to a sword)

With Turcoman Horse 'they can be ordered to charge' meaning because their stats are good enough that they can also be used as light cavalry, whereas vanilla HA are too weak to do so.

I personally prefer units like Byzantine Cavalry or Boyars; While they are slower than light horse archers which makes them not as good at skirmishing, they are much more durable and have even better attack.
And with the armor especially it makes them much better at missile dueling with all the vanilla HA the factions surrounding the Byzantines and Russians have.