We have done Disney and its probably 3rd place for us with kids (controversial to say here, I know haha).
Royal Caribbean is a great intersection of kid friendly, price friendly, and a little nicer than budget lines. For example on our RC cruise there was a free carousel my kids rode approximately 100 times, an ice skating show and free ice skating time, an aqua show, pools, a splash pad, and lots of little play areas. They also had a family theater with programming specifically geared toward parents and young kids to watch or participate in. Different ships have different activities so that is key. Some of their nicest ships go cool places like Europe!
Carnival has similar ships (again stick with longer itineraries and newer boats). The one we have booked for next year has a trampoline park and they have special build a bear times etc.
Disney is SO nice for kids who love character meets, but turns out those aren't our kids and we feel the other lines offer a lot more variety in that case. Also a lot more variety of food for the other ships.
Oh points- any redeemable for travel purchase currency is great (citi/cap1), or chase via pay yourself back. We like to book directly w/ the cruise line so we haven't booked via a travel portal.
Oh also also- we don't use the kids clubs. Our kids stay with us the full time and we never feel restricted/bored! They will play in them for open hours times (and we don't leave them because they both get nervous and we don't want to push it).