I have only sailed on Princess and Holland America, and overall, my choice is Princess.
The facilities were pretty much the same. Maybe HAL was a teeny bit nicer, but just barely.
Maybe HAL had a little bit nicer food, but we just aren't foodies and there is an over-abundance of good food (read fresh salads and veggies, and grilled fish and chicken) available in Princess. The rest is just excess for me.
The people on Princess were a whole lot younger and more active. I will admit that the HAL cruise we took was the beginning of a 34 day cruise so that might have driven up the age, but even as old as I am, those people looked really OLD.
I love being able to bring my own wine on board Princess and have parties and share in my suite.
I really love the free internet on Princess.
We now get to bypass the boarding lines on Princess so that is also very cool as well.
Overall my vote, between HAL and Princess, has to go to Princess. They also always have pretty cool dance bands. ^