I don't think its barb dromons, its dromons in general. Their RCS is too high, too strong against land units. They are basically invincible unless that player also has sailing. Catapults used to be a decent counter as well
What I hate is barbarian galleys. They come when most civs have invented fishing, which is really early. Even if I beeline for sailing, I'm still going to be 2 or 3 techs away from having my own ships, if a barb camp appears near my capital its going to raid my city for hundreds of yields and I can't do anything about it. You used to be able to embark spearmen as a sort of defense, but now galleys kill embarked spearmen in one shot.