If you post the same question on the Disboards forum you will probably get materially different answers. We have sailed 5 DCL and one RCCL cruise. We have another Disney and another Royal cruise booked for next year. Our experience might be totally opposite of others, but I'll share none-the-less.
Our trips:
DCL Wonder (Two adults and two kids both under 12)
DCL Fantasy - twice (Two adults and one >12, one under 12) (Second Fantasy both kids were over 12)
DCL Wonder - twice (Two Adults)
RCCL Anthem (2 Adults and one 14 year old) (this was this summer)
As our kids reached their early / mid-teen years that was our last DCL cruise with them - even though Disney does have the teen clubs, neither of our boys really cared from them. When they were younger the <12 clubs were great. The water roller coaster on the ship was great, but compared to a ship like the Anthem, Royal wins in this case..
We thought the service was pretty equal - but DCL was slighter better in some areas and RCCL was slighter better in some. We didn't try any of the specialty restaurants on Royal, but we love Palo on Disney. Main dining room food on both was good, but we are not foodies and pretty easy to please.
We really like the smaller DCL Ships (i.e. the Wonder). My wife and I think the late night Adult entertainment is very good on Disney, better than Anthem. Although in fairness, I have read that Anthem is a pretty poor representation of the overall Royal experience for this item.
I'm always amazed about the kid comments on Disney - it might just be because we are cruising at standard school vacation times, but both ships have lots of kids. We found that is was actually easier to get chairs and space in the adults-only area on Disney then it was on Royal. This might be because everyone on Disney has kids so the few "kid-less" cruises have space. I thought the shows were better on Disney, but again this is subjective. For instance, CATS was a long-running Broadway hit that many people love, my wife and I left that show at intermission. So just be warned that opens about show quality is subjective. Although we did think the singing voices were better quality on Disney regardless of the tune.
We liked Castaway Cay better then Royal's island in Haiti.
Our teen son loved the Anthem - tons of stuff on ship to do. So we are doing the Symphony next summer for him and my wife and I are back on the Wonder for Thanksgiving 2019.
Cost is a very real and very valid consideration. We are willing to pay for the Disney experience when it is just the two of us, but it is a materially better value and better teenager experience on Royal.
