Drapanai and their stronger rhompaia bearing cousins are excellent phalanx breakers. I might have mentioned this before many times, but I'll do it again; they come in two flavours: rhomphaia guys if you want an elite, "fewer men the greater share of honour" way of slaughtering the enemy, or just drapanai if you run by the philosophy of sheer numbers of men. Both are only good on the offensive.

To defeat them you need something strong against them: usually a line of archers and spearmen for the Drapanai, or anything that can run well and throw a missile well. Against the Rhomphaia guys you would do better to hide behind a pole or charge them in the rear while holding them with cheap troops. Most arrows seem to be harmless on them.