It depends on what you like. The rooms at the LCJ are very clean and hanseatically-minimalist, if you follow me. They have beautiful wide-plank wooden floors, a bold rug, and a sofa/chair depending on the kind of room you are getting. It's elegant in an understated way, and I love the bathrooms, which are warm and functional. The breakfast is without question the best in the city. The view, particularly if you opt for a room on the Elbe, are great. Each time I have a river-view room I go to a special wine shop in Blankenese and buy a really nice Bordeaux and have the restaurant bring me dinner to my room. The rooms facing the courtyard are also nice, and if you're on the ground floor you can sit outside. Those facing the road are pretty loud (the windows seal off pretty much everything, but don't open them at night).

The 4J rooms are a little more old-fashioned and look classically old. It really depends on your preference. All LCJ rooms are of the same renovation vintage (and I understand another one is on its way soon), while the 4J has some refurbished and unrefurbished rooms to go around. A view out to the back/middle is really not great.