The Roman Empire existed between 31 B.C.E to 476 C.E. and the Han Dynasty occurred 202 B.C.E. to 220 C.E. They existed at same times but were on opposite ends of Eurasia. They both had regions that were ruled by either kings, viceroys or governors in the name of the emperor. They were both similar in slavery, government, and their downfall. They also had their differences in religion, military, and center of power.
Both civilizations had very strong central governments which allowed for powerful and expanding kingdoms. Both empires had to develop road systems for their expanding military. The Roman army men were experienced and privileged and held high ranks in their class system and played an important role, along with the senate, in choosing an emperor. The center power for the Roman empire was generally the senate. The ruler for the Han dynasty was hereditary. The Han dynasty's military wasn't as loyal. Most of the soldiers were newly drafted and didn't have much experience. China had two capital cities which served as seats of power for emperors and they were Louyang (located in the east) and Chang'an (located in the West). The merchant class in Han was restricted by the government unlike the middle class in Rome whom were free from government constraints which allowed economic mobility. The imperial model was only revived in China later but it never revived in Rome.
One of the main differences between the two empires was their religions. Christianity, in Rome, was greatly opposed by religious institutions of the native Judaea and had to go against the official cults of Rome and also the “mystery” religions including Isis, Mithra, and Osiris. After the acceptance of Constantine, the Roman empire became mainly Christian. Constantine discontinued the persecution of Christians and supported the church. Christianity eventually influenced a lot of beliefs and decisions of the future rulers of Rome and appealed to lower class people