We did a 14day AK cruise on the Amsterdam with our 9 and 11 yr old kids. My kids absolutely loved it. We did have Club HAL, which they loved. But they also made friends with the few kids that were on the ship, and they all hung out at the pool together when not in Club HAL. One child even had an impromptu birthday party at the pool one day and invited all the kids to come celebrate. I would definitely say the lido pool was not crowded. And most of the time, the only people in the pools were the kids!! Since the roof could close, it didn't really matter what the weather was. The kids also participated in the Polar Plunge with the adults, which was fun to watch.
I would recommend going on one with a Club HAL to give them more options of things to do. The caregivers were engaged, and the kids loved going. They didn't spend all day there, but would pick and choose different activities on sea days (gaga ball, scavenger hunt, etc).
We did RCL Liberty in the past, and it was just too much stimulation for my kids. The crowds and lines were stressful, and the kids' club was always full (where they turned you away). The kids begged to go back on HAL. So we are going on a family cruise at Thanksgiving this year. My sister is bringing her 4 and 7 year olds on their first cruise. I know they will have a blast!
I have a trip review somewhere on here from our Alaskan cruise that had a lot of info about the kids' experience on the ship. I think you can click on my name and see my previous posts. But I am happy to answer any specific questions.