What differences between greek democracy during the classical era and u. s democracy during the modern era

The Athenian democracy was a direct-rule government, where an assembly of citizens would meet to debate and decide al matters of government: spending, war declarations, treaties. 
The American government is republic in the form of a representative democracy. In the United States, we elect representatives to the legislative branch: the US Congress.  The representatives do all of debating and deciding on matters affecting the nation.  The US Congress is a bicameral legislature, which means there are two houses: a lower chamber called the House of Representatives and an upper house called the Senate.  The House of Representatives is large, composed of 435 members. Seats are apportioned to districts based on population size.  The districts do not cross state lines.  The Senate is composed of 100 members, 2 per state.  Originally, senators were appointed by a states governor or legislature.  Since the passage of the 17th amendment to the US Constitution, however, senators are now directly elected by US citizens.