Nowdays, I usually tend to use all of them, crossbows, bows and throwing weapons.
Crossbows when on foot with my trusty glaive (stab enemy horse and then swing at the rider) or two hander. Quite effective against khergit riders and other mounted units. (needs good landscape, though)
Bows when riding (also on foot), effective against everything, but you need to be careful against those pesky crossbowmen.
Throwing weapons on horseback... I mostly use daggers and jarids, daggers have good damage to size-of-the-bunch ratio, and jarids have (for my oppinion) good throwing arc against other riders. My favourite target for jarids: black khergit riders with bows. Just ride behind and throw jarid through back of their head.