IMO, it's very difficult to point objectively to things that justify the Disney price premium. Objectively, Disney is solidly in the middle of the pack of premium (not luxury) cruise lines. But as you hint, that doesn't mean it isn't worth it. There are a few things that I personally think Disney does well:
- Entertainment throughout the ship is excellent, and not just in the theater. While it isn't as extensive as you'd find on resort-style ships like RCCL's Oasis-class ships, it's really good for a traditional-style cruise.
- The dining
experience is excellent. The food itself is average to slightly-above-average (and pales in comparison to premium dining on other lines), but the rotational dining concept and the MDR entertainment is great.
- The experience for kids is second-to-none. (This isn't super relevant to a cruise for adult guests, except I will note that it means that a lot of the noise and chaos that you might expect is actually pretty contained.)
-
Castaway Cay is pristine and beautiful and a ton of fun, although I actually prefer RCCL's Coco Cay just because there's more to do--I'm not a "lounge on the beach" type.
- The Disney "magic" is a ton of fun. I think this deserves more credit than it usually gets, but personally just having characters around, seeing Disney movies, and hanging out with other likeminded guests is a huge part of the fun for me.
IMO, because of that last point alone I think it's worth a try if you're a big Disney fan. But don't come in expecting real luxury. Concierge is a great experience and it may be worth it to you because it's the best that Disney has to offer, but if you come in expecting something like The Haven from NCL or The Retreat on Celebrity then you'll probably be disappointed. The Concierge lounge and sundeck are lovely (especially when the ship is full), but there's no ship-within-a-ship or large dedicated area or restaurants like there are on other lines. The Concierge hosts are great, but IMO a lot of what they do is compensate for Disney-specific annoyances like the fact that there aren't enough of the popular facilities and activities to go around (or Disney isn't charging enough for them to mellow the demand), and even then most of the advantage is that you can join the booking scrum early rather them holding back reservations for Concierge guests (although they do seem to hold back a very small number). We usually get 1- or 2-bedroom suites on other lines, but usually don't bother with Concierge on Disney because it's just not worth it for us.
I hope that's somewhat well-balanced. I love cruising with Disney and am very much looking forward to our EBTA cruise with them in May. It sounds like you're a big Disney fan so I do genuinely think it's worth giving it a shot, but if you do you should go in expecting a premium mainstream cruise line with a lot of Disney magic mixed in.