We have cruised with our kids on Carnival and RCCL, both are good for families, but in my opinion RCCL does a better job with teen activities and their kid's club is a bit better.
The Voyager class with RCCL is wonderful, with rock climbing, ice skating, roller blading, etc. We were on Mariner last April spring break tons of teens, a lot of them seemed to really enjoy the ship and activities, others just wanted to ride the glass elevators and be their version of cool.
Carnival is not strictly a party ship, if you do a 5 or 7 day cruise or do it when school is in session you will see lots of families with young children and lots of older vetran cruisers. The newer big ships attract a variety of age groups. I think entertainment is slightly better on Carnival, but we had great entertainment on Mariner last spring. I think you'd be fine with either line.