The economies of ancient Rome and Greece were similar in a lot of ways, but different in focus. The trick is, of course, that "ancient" Greece and Rome went on for a long time and developed during that period.
- The Greeks, for the most part, lived on very rocky and difficult terrain. It was not possible for them to do large scale farming of food crops, and they grew mostly what they needed to survive or olives and grapes for producing oil and wine. The Romans were in a better position for farming. The land was flatter and more fertile, and their farming skills marginally better.
- Both cultures used coinage as a means of exchange.
- Both had artisans who created products, though in Greece those who worked with fine textiles were more respected than those who worked with leather and metals. In Greece being a merchant was considered a lowly profession.
- Both cultures used slaves. The quantity varied in different parts of Greece, but their use grew and grew in Rome until almost 40% of those actually in Rome were slaves.
- The Greek, because of their lack of food, were forced to develop maritime trade much faster. This led them to have access to goods from around the Mediterranean. Ancient Rome didn't do as much trading (though it did a heck of a lot more conquering.
As for governments, again things were different.
- Greek cities, because of the harsh terrain and limited open space, developed into "city states" that were more or less united in heritage but not in politics. They all had their own rules about things. In practice, most Greek city states were ruled by some hereditary council of aristocratic men, in conjunction with a king or not. Some, like Athens, developed fairly democratic institutions. None of the city states were able to fully dominate the others and all lived fairly independent existences (as long as no outside force was attempting to conquer them.)
- Ancient Rome was not divided into separate entities. The culture had a central "hub" from which to expand. In the very early days Rome was ruled by a king, but this was supplanted by the Republic with a Senate. Just how democratic this was depends on the exact time frame. Senators, early on, were selected, while later on they were elected. Oddly enough, early on the Senate had no real power to make laws or get things done. It was the fact that the Senate was made up of powerful men who had the means to get things done that gave them authority. Ancient Rome had no real bureaucracy of government. Things changed under the Empire.