The Basilica is definately worth a visit... it is a brilliant example of the beautiful architecture that litters Budapest. The inside is lavishly decorated, although you have no idea what it is you are viewing as there seemed to be no information available (or certainly not in English anyway). The real attraction here is the tower, which may be climbed for around 500HUF (less for students, children etc.). I would strongly suggest doing so if you can conquer the stairs, as the reward is a 360° view of the city from its (joint) tallest building. A must-do in my opinion!
This review is the subjective opinion of an individual traveler and not of TripAdvisor LLC nor of its partners.