Your going to get so many thoughts here, good luck!
I would say that while I love
DCL I have to wonder if it is because its the only ship I have sailed. We are gong on our first RCCL cruise shortly and I can't wait, I'm so excited. However, as to your question,
Disney makes it different. Its their touches that make it what it is. While we have mostly had excellent service we have had bad service so you can't blanketly say its their service. Lifeguards on board are great however what parent would not be eagle eyeing their 4 year old while they are in/near the pool. That would just be irresponsible. So not sure that would be something I would pay extra for. The shows are good, very entertaining for both adult and children. Better than what can be found on any other ship? I don't know. The cabins seem to be a bit larger but from what I have seen only by a few feet. They have a split bath, some people find this very important, others, like me, don't.
I like the food but I certainly don't find it top quality. Its good, don't get me wrong, but its not amazing IMO. As for their quick service venues, I find that almost boring and not so many choices. Something I find a minus in the DCL department is that the buffet is closed in the evenings, they serve a sit down meal. The dinning rooms are lovely and have some good entertainment but it can get a little long for small children and that is where the buffet would be so handy. They do have room service but again, not a lot of variety.
People talk about the nickle and diming of other cruise lines, I have not yet found much difference. You can spend a bunch on extras on DCL such as the BBB, the new candy store (forget the name, sorry), specialty dining. They have plenty of shops where you can drop your charge card and with little ones there is a ton that they will want. Your going to find shopping on any ship you choose.
Childrens clubs, how much time are you wanting your wee one to spend there? If its only a few hours at a time you will probably be fine with any cruise line. If your planning on dropping her off at breakfast and seeing her at bed time DCL is probably best. Not sure why anyone would do this but I hear some do.
I have sailed DCl lots, many b2b Fantasy trips. I have not noticed anyone looking at me jealously. While I have seen people looking over at our ship, I and others around me have been looking back. Not out of pity but at what that ship has that DCL doesn't. I've seen some pretty amazing water slides. No one ship has it all.
These are just my thoughts, take from it what you want and discard the rest. I certainly can't claim to be an expert.
So, your delema is in deciding if you want to pay the extra for the mouse or if your okay saving some and only getting puss and boots. Good luck with your choice and what ever you do have a great cruise.