"More enjoyable and entertaining" is in the eye of the beholder!
We've sailed several times on Princess and several times on Holland America (including on the Eurodam), as well as a couple of trips with
DCL.
Here's my take:
RCCL is a much more active cruise ship experience, with activities including the rock-climbing walls and other interests geared toward the athletic and active family. This line has a LOT of fans.
Princess was fine, but I wouldn't characterize it as upscale in comparison to RCCL and HAL. Activity and entertainment-wise, it's probably between the more energetic and athletic RCCL and the more sedate Holland America. Lots of smaller eateries on the newer ships, LOTS of annoying announcements about bingo.
Holland America ship decor (at least on the Eurodam, Westerdam and Zuiderdam) is more sedate and traditional than the other two, but still quite varied and interesting. The entertainment was good, very similar to the shows and variety on Princess. We prefer Holland America's main dining room and the premium steakhouse to the Princess model of lots of smaller venues, but that's strictly a matter of personal preference. I think the quality of dining is very comparable on the two lines.
We're not the athletic-vacation types. Give us some quality stage/music/variety/magician shows, nice pools and bars, a few ship tours and lectures, a place for the teenager to meet and hang out with new friends, a comfortable library where you can relax or read or play board games or watch the waves pass by, and we're happy. We'll get our exercise at the ports.
We've got another cruise booked on the Eurodam right now. We'd also happily book Princess or RCCL if they were going to places we're interested in at a time we'd like, IF we could get a nice room at a fair price.