What is the most significant differences between the political systems of the Roman Empire compared to the political systems of Athens and Sparta?
This is a great question. Let me say a few words on each people.
Athens was a radical democracy. All the men of Athens had a role in the political life of Athens. They were jurors, warriors, politicians, and other political officers. Most of this was done by lot and changed year by year. For these reasons, Athens was a democracy in the true sense.
Sparta had a mixed constitution and their way of life was called, the agoge. First, they always had two kings, which lead the people out to battle. There was also a group of twenty-eight elders, which were inducted for life and wielded political power and had the power to veto. Finally, there were people called ephors (five of them), who acted as accountability. They looked over the kings and even the group of elders. As you can see, this was a very different system than Athens.
The Roman Empire had a supreme commander in the person of the emperor. He was a king apart from the name. He has no accountability and he could do whatever he wanted. His decrees were de facto laws. The senate was supposed to be an advisory body, but did very little.