Yes, Disney is better than Carnival, because Disney is the ultimate in entertainment. Disney is the standard that everyone else lives by. Disney has details in their cruises. Disney is also much better for family fun, because Carnival is often a party line. Carnival tries to minimize costs rather than focus on user experience more than everything.
In my opinion, Disney is better than Carnival, because they have a much more family orientated program and entertainment for the entire family. There is also less emphasis on gambling and alcohol consumption in the Disney line as well as there being more family outings and events that can be enjoyed by everyone together.