It's really a judgment call. I actually don't see much in the way of nickel and diming on RCI; primarily it's that you have to add the soda package to be roughly equivalent to
DCL in terms of non-alcoholic drinks. If you drink a lot of soda, the package is probably worthwhile. It's a relatively trivial cost in any case.
Disney has nicer ships in terms of decor, and is better on entertainment and activities, especially in the realm of exclusive Disney experiences. If you really want the stuff Disney does well, you kind of have to go with Disney, because they're the only ones who have it. If you just want a relaxing cruise vacation, RCI is a good value.
RCI does a good, solid cruise for the money. If you book some of their newer, larger ships they have a bunch of Dreamworks stuff on it, so the kids can meet characters and there are some Dreamworks-themed shows and entertainment, but it's not nearly as much of that kind of thing than Disney. Disney kind of has a "deeper bench" so to speak of characters and media properties, and has years more experience in how to handle character interaction.
Disney's kids areas are much more extensive, but since you've got teens/tweens the differences are not as stark. The bulk of Disney's special investments are in the 3-12 year old spaces, which are incredible. The teen areas on Disney's ships are better than RCI's, but it's not (to my eye) a complete night-and-day kind of difference. In the end it's a place for teens to hang out and participate in semi-supervised group activities, with video games, board games, etc. and some counselors to help guide things. Our kids never really found the teen centers interesting on any cruise line, but they're not super outgoing.
It's kind of like WDW. You can have a great time at less cost at Six Flags, but it's mostly generic rollercoasters and rides that everyone does. WDW has themed entertainment. Is it worth 2-3 times what a trip to a "generic" amusement park costs? Some say yes, some say no.
My advice is to pick one now, and then do the other one later. Only you can answer whether Disney's exclusive stuff is worth the extra money; it's completely subjective. We had fun on our Disney cruises, we had fun on our RCI cruise. We had fun on Holland America. The kids slightly preferred Disney because of the great entertainment (including movie theater, in-room movies and shows, stage shows, fireworks, etc.), but we all enjoyed each cruise for what it was.