This is a very interesting topic. During the struggle of independence in the 19th most people focused mainly on Ancient Greece (most Europeans were crazy about Ancient Greece as well) and some Greek scholars also demonstrated a negative view of Byzantines, affected by the general impression of west historians at this time. Yet, this changed some time in late 19th century officially when the most important Greek historian of his time (Paparigopoulos) proposed the scheme of continuity of Ancient-Byzantine-Modern Greeks. The role of the Orthodox Church was also important towards this. But, the mania for everything classic was still present for decades, e.g. archeologists were almost destroying in some cases the medieval and Byzantine layers to discover the classical antiquities.

Nowadays, between Greek people it is a matter of preference. Usually, people originating from modern Greece areas tend to prefer Ancient Greece and modern history (independence from the ottomans and formation of the country). On the contrary religious people or Greeks originating from Turkey (ancestors of the 1922 Greek refugees , about 20% of the population) have a tendency to love and prefer Byzantine history. In the last decades, Byzantinism becomes very popular you can see everywhere in Greece byzantine flags (the one of the double headed Persian monster :) and the original one, the red with the yellow cross and the four “B”).