What is the relationship of Athenian to modern United States democracy?

Although
both the United States and ancient Athens are described as democracies, the systems of
government are quite different.

Since the advent of women's suffrage in the
early 20th century, all citizens of the US over 18 who have not committed felonies are able to
vote. In Athens, women, slaves, metics (resident aliens), and those who did not have Athenian
grandparents could not...