The Golden Age Athenian democracy and our modern democracy had many similarities. Like our modern voting districts, the Athenian countryside was divided into units. In both these systems citizens had to be registered to vote on laws and public policies. Also, like our current democracy, in Athens you had to be 18-years-old to vote. Like us, Athenian democracy had a Council of representatives. To try to prevent corruption, they also had imposed limits on the number of terms leaders could govern.
Most likely the greatest difference between modern democracy and Golden age Athenian democracy is that of the "men only" policy. In the old age, only men were allowed to vote and take part in assemblies. Today's democracy allows both eligible men and eligible women are to vote.
The elections back then were also different. In Athenian time, they had their main elections via lottery. They thought this would help to control campaigning and election corruptions. In today's democracy, when we elect someone all eligible citizens can vote and the majority wins. Also, unlike now, active military leaders were elected to governing positions. Back then they believed it created a stronger government.
One major difference is that in the Athenian legal system, is that there were no lawyers. Everyone had to argue his own case. The accused could hire someone to write their defense speech, but they had to present it themselves. Wherein today lawyers are everywhere...