Strategypage writes of the debate:
American Navy commanders are coming to believe that they will have to replace many of the manned aircraft on carriers, with UAVs, if carriers are to survive in combat a decade from now. That's because potential enemies will have access to UAV technology, and better missiles as well. Without the advantages of UAVs (greater endurance, stealth and lower cost), aircraft carriers won't be able to defend themselves well enough to prevail. These are the same kinds of calculations that drove naval planners in the 1930s, to abandon dependence on battleships, and plan for heavy use of aircraft carriers.
As I noted recently, however, it looks like the Navy has decided to settle the debate by building both types of carriers, by making new amphibious ships (LHA-R class of amphibious warfare platforms ) that will be bigger than other countries' carriers and much smaller than our super carriers:
These will outclass anybody else's actual fleet carriers. And we don't even really count them as carriers. Yet they'd do perfectly fine as carriers in a pinch and would be able to carry out various escort and ASW tasks quite well and free up the big decks for offensive action.
Which I suppose makes perfect sense. When carriers supplanted battleships, we didn't scrap all our battleships. Indeed, we built the most advanced battleships to date during World War II. These ships still had great value in their niche market despite the new dominance of the carriers.
And as I've noted before, our super carriers will only slowly lose their dominance based on enemy development of network-centric warfare at sea. Until that happens, our carriers are still the most powerful individual ships on the planet.