The major difference is that the Greek democracy gave more power to more people than the Romans did. The Romans had a direct democracy that got to vote on a lot of laws and have a part in carrying out the laws. Roman laws were made much more by elected officials (Senate) and carried out by government officials like consuls and censors rather than by more ordinary people.
Both were very democratic for their times, but the Greek system was more of a direct democracy and the Roman system was more like our representative democracy.
I hope that this is the answer that you were looking for and it has helped you.
