In real life, aircraft carriers eventually made battleships obsolete. However, Civilization 4 and many other games make the battleship the main modern navy vessel.
How about in Civilization 5? Do aircraft carriers and aircraft succeed over battleships?
Also, what about naval warfare in general?
Aircraft carriers will far and away succeed against comparably numbered battleships for 4 big reasons
1: The ranged combat strength of fighters is stronger than the ranged combat strength of battleships
2: The manual has not confirmed that battleships have interception ability. However, it has confirmed that destroyers and missile cruisers do have this ability. This means that battleships, if not escorted by destroyers, are defenseless against carrier-borne fighters
3: A carrier with 3 fighters can attack a battleship 3 times, whereas a battleship, if it is in range of the carrier, can only attack once
4: The range of fighters is far and away longer than the ranged bombardment range of battleships.
In terms of naval warfare, carriers will be at a ridiculous, and yet entirely realistic, advantage against battleships.
That said, battleships will quickly become obsolete as civilizations focus more on air power as the main tool in establishing dominance over the sea, and as the main system for delivering fire support to land units
The only way that battleships will be useful is in the times before civilizations build aircraft carriers, or as fire support assets for when there is too much anti aircraft near the beach.