I can’t speak for HAL or Princess (other than what I’ve read), but I can speak for Celebrity.
Demographic: The crowd will be older on Celebrity than Disney, but likely not as old as HAL. Also, if you aren’t travelling during school holidays and if it’s a longer cruise, expect a small number of kids. There’s about 150 people in my roll call for my upcoming 2 week Celebrity cruise, and we’re the only ones so far with a child. I’m fully expecting perhaps as few as a few dozen kids on our cruise and I’m fine with that. My son is introverted and will do well with the peaceful environment and extra attention that comes from an uncrowded kids club. An extroverted child might not feel the same way.
Cabins and Decor: The win goes to Disney due to its classical elegance and cabins designed well for families. But Celebrity (particularly S-class ships) provides some good competition with its beautifully modern ships and cabins that have sofabed space for kids. I’d love to try Princess one day - on paper it looks great. But where it always falls flat in my online comparisons is that it’s cabin categories (lower than a mini-suite) look really cramped if you’re a party bigger than 2. Plus the decor on some of Princess’ ships does look a bit dated.
Evening Entertainment: I much preferred Disney’s evening shows.
Daytime Entertainment for adults: I think the slight edge goes to Celebrity. I’m not interested in ‘Name that Disney Tune’ trivia and found Disney’s organised adult activities severely lacking. Celebrity does offer a bit more, but not without mentioning that some of Celebrity’s so-called ‘enrichment’ activities are thinly veiled sales pitches (avoid any spa and gym talks). On paper, Princess looks better than both.
Kids Activities: This will be the first time my son has sailed with us on Celebrity, so I can’t make a direct comparison of the kids clubs, other to say that I think he will enjoy Celebrity’s as much as Disney’s, but for different reasons. However, when you also throw in the likes of the Aqua Duck, Detective Agency, Character Meet and Greets etc, Disney obviously offers a lot more for kids. Only you know if your child needs all these extra things to keep her entertained, and if so, I think the suggestions above to try NCL and
RCCL are good ones.
Food: The win goes to Celebrity. Apart from Palo, I was really disappointed by Disney’s food. I found it under-seasoned and unmemorable.
Value for Money: The reason I’m a repeat Celebrity customer and not yet a repeat Disney customer is cost. Dollar for dollar, I think Celebrity offers quite a bit more, especially if you book during a promotion that includes 2 or more perks (one being the drink package).
Onboard Service: Tie. I’ve found service to be exceptional on every cruise I’ve been on, even the low budget cruise lines.
I hope this helps.