After 2 cruises with Princess, we decided to try Norwegian based on the port that it departed from (New Orleans). Overall, I will say that we (and several others we talked to on the cruise) prefer Princess in every category.
Some positives first: When visiting Roatan, Honduras, you MUST do the Maya Key Private Island excursion. This was by far our favorite stop on the cruise, and we would have been happy to spend several days on the private island!! The beach, snorkeling, animal rescue sanctuary, and picture spots were only some of the amazing things we experienced - and the buffet-style lunch was delicious! Onboard, we really enjoyed the "Elements" show on the last night of the cruise and the great deals on 3-liter bottles in the liquor shop (we bought them as bar decorations :) ). Eating at Cagney's Steakhouse is another MUST - delicious food with great selections! Our stateroom steward was wonderful, and we liked the "self-disembarkation" option that let us carry our own bags off of the boat. Though there weren't formal nights onboard, photographers were set up every night to take pictures, so you could dress up any time (we enjoyed this!) and take photos.
In Costa Maya, we got a taxi to the "downtown" area and enjoyed time on the beach and a $25 hour-long massage. Be warned, though - they "don't have change" so carry many small bills so that you don't end up leaving a huge tip, and there will be people trying to sell you something all the time (this got very annoying after several hours)! I would recommend going back to the boat or dock area for lunch. Belize: Altun Ha ruins and Olde Belize River tour was just ok. A VERY long shore excursion, and the lunch we were served wasn't great. I wouldn't recommend this excursion, but Bacab Jungle Park (where we had lunch) looked nice and enjoyable with its pools and lounge area.
There were many things that made our Norwegian cruise not as positive an experience as Princess, though. The service we received at dinner in the main dining rooms was not always good - the first night our waitress rushed us through the meal and did not check on us at all throughout the service. We had to wait quite a long time to get our luggage when we boarded the ship, and we had pieces of luggage come at different times throughout the night (I received my last suitcase 7 hours after boarding!). Also, the luggage was not handled with care (one of our bags had the handle ripped off, and initially Norweigan refused to give us the full amount of the bag's worth!). There is only one pool on the Star, and it was always SO crowded that we never got to enjoy it. In 8 days of cruising, not once did we have someone approach us in the buffet area at breakfast to ask if we needed silverware, a drink, etc. - guess we were spoiled with this by Princess, where everyone was very attentive. There also wasn't as much variety in the dinner menus - more food options stayed the same every night than changed, which we found to be the opposite of Princess.
Other random comments: Bingo cards were unbelievably expensive - we didn't play once!! We did not eat in Aqua but very much enjoyed Versailles. We had an adjoining room (not by choice) and hated it - we could hear every little sound that our neighbors made! Not sure if this is true of non-adjoining cabins or not... I overheard from other passengers that many of the shows/games were more risque than advertised - just be warned.