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Bohemian Halbs deal 25% extra bonus damage vs cavalry. This allows them to kill Paladins, Heavy Camels, and Elite Battle Elephants 1 shot sooner than generic Halbs.
In terms of 1vs1 DPS:
Japanese Halbs are generally the best in the game - they kill most cavalry (and other non-cavalry units) faster than Bohemian Halbs.
Bohemian Halbs come in 2nd place vs cavalry (but are generic vs non-cavalry units). Burmese Halbs come in 3rd place vs cavalry.
Obviously there are some honourable mentions (for those "it depends" scenarios):
Lithuanian and Celt Halbs move faster (and so can chase down cavalry).
Slav Halbs have splash damage (and so will do well in group fights, but are generic 1 vs 1).
Goth, Byz, and Korean Halbs are cheaper (and so trade more cost efficiently).
Teutons Halbs have higher melee armour (and so are tankier).