The main differences between Ancient Greece and Medieval Europe can be seen in different sectors of society. First of all, political systems changed from Greek's democracy and the idea of the republic to monarchy and nobility driven kingdoms, which in retrospective were very similar to former Greek city-states, except that during the middle ages there the king was the full sovereign of the land while in Greek civilization they believed that the sovereign was the people.
Another crucial element to take in consideration is the change of faith, monotheism and Christianity in particular changed the entire socio-political structure of society, while Greek politics were secular, during medieval times Christianism became closely tied with politics for more than 500 years, giving kings divine rights which allowed them to reign with absolute power. The development of Christianity in Europe also brought an important change in people's mindset towards other religions, there were perseptions and trials for heresy, apostasy, etc. It also unchained a series of wars called the crusades in order to recover places that were considered holy by Christianity.
In the economy sector, during the middle ages slavery was no longer practised as it was in Ancient Greece, but it became into servitude through feudalism, the landowners will offer protection and land to peons and servants in exchange of revenue taxes from whatever is produced in that lord's land.
In society there was a change of paradigm regarding on how to live life, Ancient Greeks considered life should be lived at its fullest given the limited amount, the idea of an afterlife wasn't focused on how your actions affect your destiny after you die. Christians during the middle ages were acting on the belief that how you behave in this life determines whether you go to heaven or hell. Therefore, people became more cautious, prudent and modest in their daily life in order to guarantee themselves a place in heaven.
