What is the difference in the political structure of the Roman republic and Imperial Rome?
The difference between the Roman Republic and Imperial Rome are significant. In fact, there are too many differences to go into detail. So, I will only mention the most important differences.
First, the Republic was a revolt from the regal period of Roman history. Therefore, the basic idea behind the Republic was the notion of parity or collegiality of power rather than the absolute power of one individual. So, for example, the highest officials of Rome were in pairs (consuls), so that there would not be one ruler. This structuring could also be seen in the Praetors and Quaestors. Imperial Rome was huge shift from this, because the Emperor was very much like a king. Rule was in one person.
Second, in the Republic, there was a one year term for office. To be sure, some individuals got reelected, but by and large no one person held power for long. Imperial Rome changed this completely as the emperor had power as long as he lived.
Third, in Republican Rome the senate was a vital force of political power. One might argue that the senate was the most powerful. However, with the advent of the emperor, the role of senate diminished greatly over time.