The Shrek takes on Mickey thread is excellent and really gives you the information you may be looking for. It is long and took me several days to read through it. Some of the earlier posts in this thread also give some very good tips. I'll share my opinion on this as well.
We sailed
DCL to Alaska in August of 2011 and recently stepped off the
RCCL Freedom just last week. We're going on the Wonder again in September of this year, because the price is right.
Disney caters to families (not just children). There are subtle but important differences. For example, the drink stations on Disney. Yes, the other lines offer unlimited soda for a nominal fee, but they don't always have a drink station and where RCCL does, you have to use their special mug. The shows on RCCL are excellent and kids do enjoy them, but not as much as they enjoy the Disney shows. For example, Marquee on RCCL was very well done and the talent was incredible. The show quality could not have been better, but the show itself was a walk through Marquee-level broadway shows like 42nd street (opener). Very flashy but unless you are an adult or theater geek (I say that in a kind way), you won't make the connection and it will seem boring and disjointed. The final show, "Once Upon a Time" was much better in that area. The staterooms are slighlty larger on DCL too and they have many more options that include a tub for bathing small children. Every little bit of space helps when you have a family sharing one room. The rotational dining keeps kids engaged as it is something different every time. These touches give DCL a decided edge when it comes to family cruising. That said, remember that RCCL and Carnival both have many more ships and as a result have much more to choose from, and at much lower prices, both of which are very important to families too. As a result, both lines carry more familes on cruise vacations than DCL.
For our recently completed cruise on the Freedom, we were able to pay for our entire cruise, including airfare and excursions, for the same cost as the base cruise fair on the DCL Fantasy Eastern that we had originally booked. In general, the price difference is between $300 and $700 per person for the same itinerary and similar size ship (DCL compared to RCCL or Carnival). The savings could be greater as you might find a "better" option with more to choose from. For example, we encountered a Carnival ship (Magic) on our Western itinerary that sailed from Galveston. We also saw a ship in Cozumel that sailed from New Orleans. For those that live in that region, they may be able to save on airfare and still enjoy a similar cruise experience. While Disney will sail out of Galveston, they still only have 4 ships, so options are limted. If you want to go to the Western Caribbean aboard Carnival, you can choose to sail from Miami, Port Canaveral, New Orleans, Ft. Lauderdale, Tampa or Galveston. Eastern sails from Charleston as well as many Florida ports. There are options from Puerto Rico as well. Plus, while you can choose a 7-day itinerary, they have 4, 5 and 6 day choices too.
The bottom line is this. The prices for DCL are based on demand and there remains a very high demand for their ships and itineraries. There is only ONE place you can go for the DCL experience. Only the passenger can decide if that experience is worth the premium. If you are a family and you can afford it, I say go for it. You won't be disappointed. But if you are pinching pennies and cruising DCL means you will have to cut back on excursions in order to afford it, then it isn't worth it.
In my view, if you REALLY want a Disney experience, then sail RCCL out of Cape Caneveral and extend your cruise vacation to include WDW Magic Kingdom for a couple of days. If you try to do all the WDW parks then you are going to need more than two days. Get there early, visit WDW and then set sail. You can do two days in the WDW parks (maybe three) AND the RCCL cruise for the price of a
Disney cruise vacation without the parks.