Don't expect passengers on Princess to be older overall than those on Carnival. It really depends upon the time of year and the itinerary. In June of last year, there were over 200 children aboard MV Royal Princess with their parents for a 12-day cruise in Europe! There were some older passengers, too, but most assuredly nowhere near as many as you would expect to find aboard a ship of Holland America Lines.
That said, Princess Cruises is a premium cruise line that tends to attract a somewhat more affluent crowd than the mainstream lines. You'll see a few men wearing "T" shirts and/or jeans, but "golf" or "polo" shirts (with collars) with dress shorts or slacks (dockers, etc.) are more prevalent. You may find more jeans in Alaska, especially when the ship is in port, due to the nature of some of the excursions there.