Simply put, range. Think of it like this: the 16" guns on the USS Iowa can put a 1000kg shell about 40 kilometers. That's powerful. The USS Enterprise(of WWII fame) can launch a wing of SBD Dauntless dive bombers to deliver a similar payload, only now you have a range of almost 2000 kilometers. Nowadays, the range is even longer: The USS Nimitz can launch a Super Hornet with a range of a little over 2000 kilometers, which can in turn launch a Harpoon missile with an extra few hundred kilometers' of fuel for good measure. Plane and missile technology can get better, but gun technology is stagnating. Even with rocket-assisted projectiles and the like, guns have a lot of catching up to do.

A Battleship is good at one thing and one thing only. Delivering warheads onto enemy foreheads out to about 20-25 miles.

And Air Craft Carrier and its Air Wing can do that with even greater range, and more precision and control, in addition to not just delivering bombs, but torpedoes, depth charges, and most any other ordnance required. And can also project power in a much greater circle than a BB could.

It should be noted that it wasnt anything inherent with the CV that led to its dominance, but that aircraft had finally advanced to the level that their payloads could truly destroy enemy ships that spurred the gradual change.