Seeing all the different countries/areas of the world. Although sometimes you wish you had more time in some of the locations and other times you want to get the hell out. Gives you a good idea of places you may want to visit for a extended time period.
I would never do Royal or Carnival. Im kinda a cruise snob and like paying more for the cruise to get better service. Celebrity is my #1 choice always, although I have been on Princess also and they were pretty decent. The 2 you listed are geared towards the younger crowds IMO and I cant stand being around them sometimes.
As for itineraries, it all depends. Im pretty open for anyplace. Although I love the southern Caribbean.