I think your premise is wrong. If you are taking the period of say 500 BC to 500 AD as "antiquity" and 500 AD to 1500 AD as "post antiquity", let's count great empires:

Antiquity: Rome, Achaemenids, Macedonian/Selucid, Parthians/Sassanians, Han/Jin Dynasty, Maurya. I count 6.

Post Antiquity: Umayyad Caliphate, Gokturk Khaganate, Empire of Charlemagne, Mongols, Sui/Tang dynasties, Yuan dynasty. I count 6.

Admittedly there are counting issues here, obviously the Yuan dynasty was comprised of Mongols too, but I think it's distinct enough. There are plenty of edge cases: Fatimids, Ottonians, Byzantines, Ottomans, Dehli Sultanate.