We went to Alaska on the Amsterdam in June 2002, and on the Magic on December 2003.
HAL is a class company, just like Disney. I have said before here that HAL is the closest to Disney of the lines I've been on. (NCL,
RCCL & Paquet).
I can't comment on the kids programs on either ship, even though my kids went on both cruises. Both times they opted to stay with my wife and I and do "adult" things. Both were really family vacations, time for us to be our kids friends, not mom and dad for a week.
Wait staff was great, especially with the kids on HAL, as with Disney. There were fewer kids on HAL, but still a lot, so access to equipment the kids wanted to use was a bit easier on HAL.
There are two advantages HAL has over Disney.
1) As with most lines, the shows are always after dinner, even late seating, where as Disney has the Late Seating show BEFORE dinner so you have to hurry a bit.
2) And again, as with most lines, HAL uses a more traditional system for disembarking from the ship on the last day. You are asked to meet in a specific public room after breakfast. You get off the ship based on when your flight leaves. We were in the very last group because we had a 2 pm flight, and were off the ship by 8:45 am. On the Magic, with everyone trying to get off the ship at once, it took us until 9:15 to get off, and I heard at the airport that the last group didn't make it ashore until 10am.