It depends on what you mean by advanced. Ancient Egypt was the most stable and longlasting. That must count for something. The Greek and Romans in terms of military technology were much more brutally efficient but did not last nearly as long.
I think the most advanced civilization would be the one where things like literacy was the highhest. And where the average person had a right to access to the privileges of new technology which leads to a better standard of living. Ancient Egypt with its low literacy levels and rigid God-King concept does not seem to ofer thsese opportunities; however their efficicient bureaucracy assoociated with the Nile floods and vast agricultural output may have meant an easier life for the average person.
However the Greeks at least in theory with their Humanistic concepts and ideology seem to be an ideal. However relaity very often fell short of that ideal. I think the Arabs with a religion and culture based on the concept of memorizing the Koran (making it very literate) and Monotheistic humanism comes the closest to reaching that ideal. That is if arab-Islamic culture counts as antiquity.
However i must say I dont know much about other cultures such as the Persians, Chinese, Hittites ,Mesopotamia etc. and how well they reach those standards.