I've been cruising Princess since 1974. I've been on one Holland America cruise a few years ago and absolutely loved it. I will even say I think HAL has the edge in quality and service--and it comes at a slightly higher price. I haven't tried RCL yet.
I think Princess has the right combination of quality and value. On a 7 day Caribbean cruise I think you'll find the night life a little livlier on Princess. And while I really do like the more traditional ambience of the HAL ships, or at least the one I was on--Veendam--I do think the Princess ships are more elegant. The one thing that keeps me from cruising HAL more often is the lack of affordable balconies on the smaller ships. Princess definitely has the edge there.
I think you will find that Princess is "luxury like Holland America but fun like RCL," without all the bells and whistles.