Unusual quality
Hotels can be comfortable, have nice rooms, interesting designs, good locations, etc. etc.
Library hotel as all of these qualities so there's no need to say more about that. But the main reason for staying there is the 'library' aspect. First, it is inetresting to see which room in the Dewey system you will be allocated. Second, it is fun to discover the books in the room. Third, it is as much fun to browse the bokkshelves around the house. Fourth, when suffering from jetlag, picking a book at random and spending an hour so reading helps. 
The intellectual experience is thus what makes the hotel different and, for us, a first choice in New York. We are waiting for other Library hotels!