What do the Coliseum in Rome and the Hagia Sophia in Constantinople tell us about cultural differences between these two empires?

At its zenith, (Western) Roman culture could be typified by its primary interest in entertainment, hence the immensity and majesty of the Colloseum, a structure built for entertaining the public. Eastern Roman culture (Byzantium), on the other hand, centered more around Christian religion, hence the immensity and majesty of Hagia Sophia (Saint Sophia), a structure built for public, religious worship.