What is the difference between the Roman Republic government versus the Roman empire government?

The answer said by huntress99 is right. it is the correct answer.

In the Republic, political power was in the hands of the Senate, mostly composed of the Roman aristocracy. There were a number of theoretical checks and balances on political power, but many of these were more apparent than real, the senior Roman aristocracy essentially running Roma largely for their own benefit through the Senate.

Under the Empire, all political power was in the hands of the Emperor, an autocrat who ruled with Absolute power.

However, under the emperors, the wealth was spread around more evenly. Expansion of territory under Roman control made the empire much richer than the republic, and a number of imperial construction projects - the Colisseum, Circus Maximus, Trajan's Forum, the Baths of Caracalla - provided services and free entertainment to all in Rome, and the infrastructure of imperial provinces was widely improved under the emperors - something generally given a much lower priority under the Republic. The Emperors widened Roman citizenship to the provinces, giving more rights to more people, and in Rome itself the dole of free bread to citizens was regularized and increased.

All in all, life throughout both Rome itself and the empire was better for more people under the emperors than it had been under the Republic.