Aircraft carriers project mighty naval power. The United States has nearly a dozen of them, making them the most powerful Navy in the world. China, by contrast, has only one of these things and it's still considered experimental technology for them. Also, you can put nuclear missiles on those carriers, and send them anywhere you want, which makes them better than just a missile by themselves.
Yes, an aircraft carrier is better than a nuclear missile. Nuclear missiles deliver wanton destruction to large areas, thus costing the lives of many civilians. An aircraft carrier manned with aircraft that contain traditional payloads allows for surgical strikes where civilian casualties are kept at a minimum, while the objective can still be completed.
Yes, an aircraft carrier is better than a nuclear missile, because an aircraft carrier allows a military to deploy weapons more precisely. A nuclear missile can cause a lot of destruction, but it is very powerful. An aircraft carrier allows the government to select targets more carefully, because it allows the government to minimize loss of human life.
This question heavily depends on the situation that they are being attributed to. On a one-to-one basis, one aircraft carrier definitely has more utility than one nuclear bomb. An aircraft carrier can bring a large air force presence to anywhere on the globe. Those airplanes can then drop smaller bombs on an opponent. One nuclear bomb only has one use, and brings much more dire consequences than an aircraft carrier.
Aircraft carriers have been the backbone of the navy for the past few decades, but the awe they inspire can't compare to the seriousness of nuclear weapons. Aircraft carriers are valuable tools of war, but nuclear weapons, by their simple existence, have prevented wars from ocurring in the first place.
The aircraft carrier and nuclear missile are designed for two completely different purposes. A nuclear missile causes devastation over a large area. Aircraft carriers attack individual and group targets without causing as much devastation. It's impossible to call one better than the other, and there's no reason to make such a decision.
An aircraft carrier is not better than a nuclear missile. A nuclear missile can do a lot more damage and take out a wider area. I guess it depends on what you are trying to destroy but a nuclear missile is something that you do not recover from very well.