I answered a similar question here a couple of weeks ago. To summarize my points in the answer, battleships are poor at dealing damage and protecting power, and are both very vulnerable and very expensive. Battleships effectively can't threaten anything beyond the range of their guns, while aircraft can hit targets far over the horizon. Battleships deliver a limited amount of ordnance compared to aircraft. Battleships are large and expensive, requiring large crews and a lot of materiel. However, they do not offer increased protection, being very vulnerable to modern weapons (mainly torpedoes and nuclear weapons).