This plaza is special because in the same view you get three different cultures: Aztec, Spanish, and Mexican.
Yes, there is a difference between Mexican and Spanish, the Mexican culture is a blend of the Mesoamerican people with all the Spanish word. There are things unique to Mexican culture that has not been reproduced in other conquered countries in Latin America or the Caribbean.
In Plaza de las tres culturas you find the encounter of these differences with the Aztec ruins of Tlatelolco, the Spanish temple, and the Mexican modern (1970s) buildings, and concepts.