I have teen daughters, and we have done both Carnival (4 times) and Disney (5 times) through the years. We presently have a mother/daughter Carnival booked for this summer to celebrate graduations and reconnect before eldest leaves for college. I booked the Carnival because, with our finances and job outlook and college coming, I wanted cheap and selected based on ports. With Disney, the cruise is about both the ship and destination, with Carnival it is all about the ports, at least for my family.
The main difference, at least the one that my family and I notice, is that the whole atmosphere on Carnival is different. While on Disney, we feel that family connection time is really the focus, on Carnival it is party time. We are not drinkers, we don't go to the casino, and we don't care for the Vegas-style shows (with requisite thongs and suggestive dancing). Others do like it, so they find lots to do on Carnival, but my family always finds ourselves busier on Disney, as we find more to do as a family while on the ship. However, my children have never been ones to spend time in the clubs unless it was for art or science projects, no matter which line they are on. I guess they think if they aren't with mom and dad, they might miss something? 'Cause mom and dad are such fun to be around, ya know!
I will say that my eldest daughter's experience with the teen group was terrible. She felt it was all about trying to get the boys and girls to pair up and not bother the counselors, and she especially did not like the "get-to-know-you" game of girls chasing down the boys to remove the colored bandannas from their pant loops. Other kids did enjoy it, but my daughter is a little more conservative and the teen group was just not her style on Carnival. My youngest, however, would probably love this game, so we are keeping her out of the 14 year old group!
You may want to try Carnival if price is an issue, but yet you really just want to get away with your child. If price is not an issue, Disney is the way to go, at least it is for my family, even with older teens now.
In fact, when I surprised my daughters last week with the cruise, I had printed up a little booklet with a picture of the Carnival ship on it and all the ports we were were going to on the inside. Both my daughters, as soon as they saw the ship, before really looking at it, started jumping up and down, whooping it up, and singing, "We are going on a
Disney cruise, we are going on a Disney cruise". I quickly told them no, it was Carnival. While they are still happy to be going on a trip, they do not whoop and sing about Carnival. They are excited planning our port excursions and which books to bring for sea days on the cruise, but Carnival does not bring out the joy that a Disney experience does, at least not in my family.
There really is nothing wrong with giving another line a try. Just be prepared, know the differences so you aren't surprised (like when you see the family show and it is skimpy costumes and sexually suggestive dancing, or disorganization is rampant at all levels of service, etc.), and remember that Disney and Carnival are different lines with different atmospheres. You may find that you actually prefer Carnival, which would be great, because it is alot less expensive than Disney, and your pocketbook will be very happy! Or you may find you and your daughter will only want to go on Disney, but at least you will know. Trying new things is part of the fun of living!