I say the ships do a really good job of creating the Disney experience. Each of the ships has Broadway-style shows that relate to Disney in some way, family-friendly events, character meet-and-greets, etc. It's kind of like the Disney Parks, only on the sea. Oh and did I mention the all you can eat food?
My favorite part of Disney Cruise Line is the character meet and greets. The characters on the ships are more widely available. Also, there are only about 1,000 people on the ship for the length of the trip providing extra opportunities to see the characters. In the parks, there might be 10,000 people (rough estimation) that see a character in a day. I think on the ships, the character experiences are a little more personal.