This is a good, but broad question. Not all Greek poleis (plural for polis) were the same. In fact, there were great differences between them. For example, Sparta was very different than Athens. Athens was a democracy and Sparta had two kings, a counsel of elders and ephors, who watched over the kings. So, it is hard to make generalizations about Greek cities. With that said, it is still possible to talk about the Roman Empire and how it was different. I would say that the Roman Empire was different from the poleis of the classical Greek world in two main ways.
First, the Romans had a vast empire. The Greek had small city states. In light of this, the Romans had a government that was able to control a vast amount of land. They had provincial governors and other officials that enabled them to rule in distant places. Second, the Roman culture was one that assimilated other cultures very easily. The Roman even gave citizenship easily to others. The Greeks, on the other hand, were very insular and rarely assimilated others. The second point, in my opinion, was the most important.