If you can snag a Carnival Cruise that includes Half Moon Cay in their itinerary, the choice would be a no brainer for me. Half Moon Cay is the most spectacular beach I have ever been to. The day there is unbelievable - you never want it to end - especially for kids. Calm, shallow water, sand is like whole wheat flour. It's rated one of the best private islands of all the cruise lines and Carnival borrows it from Holland America Lines on some of their itineraries.
agree 100% and with the money you save booking CCL you can rent a cabana

. We enjoy CC but HMC is our fav private island - so far

When pricing I find
DCL to price out 2-1/2 X more than similar length DCL.
DCL is our fav cruise line, and it's an indulgence in our travel budget that I have to stretch to cover my habit lol. We only book it:
* when rates 1st come out (typically the cheapest opposite how most cruise lines discount heavily closer to cruise dates)
* an inside cabin (oddly the insides on the Dream can wind up costing more than a OV due to popularity of the porthole)
* with onboard booking discount/credit res (which we wind up moving forward to different cruise at least once).
We've sailed CCL several times, mostly for the itineraries but past guest/military/early booking discounts are hard to beat. You need to do your research on the ship, check out reviews on cruise critic. I'd hesitate before sailing NCL again, not so on CCL.
CCL has a lively crowd who came to have a good time, but i've seen the sloppiest drunks aboard DCL (I bar-tended for years, apparantly amatuer drinkers who overindulged) combine with fact you can bring liquor aboard DCL it can cause problems vs CCL who only permits a bottle of wine per adult.
jmho, a 3 day cruise flies by so fast if you haven't sailed yet, i'd go with CCL and book an inside unless you have a sea day to enjoy balcony.
You cannot fairly compare a disney value to deluxe resort. If you can swing it, BCV has an amazing poolscape. Perhaps renting points from a DVC member (not a solicitation!) might be the way to go for your family of 5.
good luck.