For a 7 day Caribbean cruise, it's my experience that HAL and Princess have very similar demographics.
Based on their size, more elegant ambience, and imho much better food and service, if choosing between the two, I'd easily opt for HAL.
On of my favorite things about Princess was the 24hr. Horizon Court area, but I understand they're no long open 24/7.
Princess has better entertainment I think, but the horrible design of their showrooms makes me nuts, when people have to sit in the aisles and stairways.