Both were city-states
Both had mountains surrounding their land, but the alps did nothing to help the Romans. So as such the romans had many invasions.
The Greeks did not permit the building of empires, while the Romans did.
Over time, Greek culture combined with Roman culture to make a Greek culture with Roman overtones.
In Greek religion, the gods were based on personality traits. In Roman religion, the gods were based on objects instead.
In Greek Mythology Gods were beautiful in appearance, In Roman Mythology gods were only pictured in the mind.

Both Greece and Rome are Mediterranean countries, but the terrain of the two is very different. The ancient Greek city-states were separated from each other by hilly countryside and all were near the water. Rome was inland, on one side of the Tiber River, but the Italic tribes (in the boot-shaped peninsula that is now Italy) did not have the natural hilly borders to keep them out of Rome.
Art in Greece is considered to be Superior overall as Roman art was merely imitation of Greek Art.
Greeks and Romans both used agriculture as a key driving factor of their economy, with Greeks using wheat and the Romans making wine from grapes and Olive oil from large olive farms.

 The social classes of Greece and Rome changed over time, but the basic divisions of early Athens and Rome consisted of:
Greece
slaves
freedmen
metics
citizens
women;
Rome
slaves
freedmen
plebeians
patricians.

Greek (at least Athenian) women were not citizens; Roman women were. Both societies were also divided according to wealth.

In Greek families, the woman was the stay at home mom. but in Roman families the mother could own property and go about as they pleased. Roman women were citizens but Greek women were not.

Originally kings ruled Athens; then an oligarchy, and then democracy (voting by the citizens). Kings originally governed Rome. Then Rome enjoyed a mixed Republican form of government, followed by emperors.