Since Princess and HAL generally have an older group of passengers, would you expect to see nicer casual clothes than I saw on Carnival? I was surprised at the "grungy" clothes I saw on our Caribbean cruise last year on Carnival.
My rule of thumb when packing is it comfortable. I bought lots of new clothes for my cruise and threw in some my old ones, I found myself washing my old clothes to wear over and over again..Next cruise I will definately bring my old comfortable clothes and of course the dress up ones. It's your vacation why not be comfortable
Our cruise to Alaska was just our second. The first was on a Celebrity ship with 2nd. on a brand new RCI ship. The inagural was also the birthday celebration of RCI. I even contacted our local district sales manger who assured me the dress for Alaska (especially formal nights) would be "less" dressy. They were wrong! Jeans, cotton sweaters or sweatshirts, sneakers are fine by day, but evening casual was still pretty nice sports clothes. One distinguised grandfather wore the most beautiful colorful sweater I had ever seen on a man. When we priced a similar one in Juneau, it was priced at $650! A little out of my price range. Do bring comfortable clothes that you enjoy getting dressed up for the evening in. Also, most ships have a spa and often a dome covered pool, so don't forget your swim suit. Gloves and a hat are a must for touring.
I have my regular California summer clothes. I start getting them organized several weeks before sailing. I break down and starch and iron them. Really makes a difference. Nothing that is faded, limp, stained or pilled goes aboard.
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.