Well I have decent result with long bow... except against armored unit wich is somewhat weird... because historically longbow where the Knights killer not the too slow crossbow...
Things that could help is to add a chance to hit the horse
Bow weakness strike me when I compared the composite, long and current bow. then I look at a basic shortsword and saw his damage range to be from 5 + 10 strengh = 15 + 2D6* so they are basically better than any bow.... wich is somewhat surprising ....
What also is annoying is that bow already are weakened by their great miss rate at medium/long range so it seems balancing enough.
Also keep in mind that bow user strength DID greatly affect the weapon damage capability.