There were two major similarities between the Roman Empire and Han Dynasty: the large land areas under their control and the fact that both empires peaked at around the same time in history. The differences are also fairly evident. Rome expanded its rule over continental Europe, Britain and the Near East, making it a heterogeneous, polyglot empire. The Han dynasty was comparatively monolithic, even at its greatest strength.
The Roman Empire arose as the successor to the Roman Republic following a civil war in the wake of Julius Caesar's assassination in 44 BCE. Octavian was proclaimed as the emperor Augustus in 28 BCE; his dynasty ended with the suicide of Nero in 67 CE. For the ensuing three centuries, the Roman Empire remained politically unified, but it never overcame two fundamental problems: its lack of a formula for the peaceful transfer of power and the growing military prowess of the Germanic tribes. After Rome's defeat at Adrianople in 378 CE, the decline and collapse of the Western Empire quickly followed. Alaric the Visigoth sacked Rome in 410 CE. Vandals plundered the city in 455 CE, and in 476 CE the last Western Emperor, Romulus Augustus, was deposed.
The Han dynasty was the historical successor of the Chin empire, established by Shi Hwang Ti in 221 BCE. For two centuries, Han emperors ruled over an expanding kingdom connected to the West via the Silk Road. The latter half of the Han period was marked by political instability and natural disasters, but not by foreign invasion. Around the year 10 CE, an official named Wang Mang usurped the throne of China for about 15 years. After a brief civil war, Wang Mang was killed, and the Han Dynasty continued until 220 CE. At this point, central government dissolved across China. Political unity wasn't reestablished for over 350 years, until the Sui Dynasty rose to power in 581 CE. Between the end of the Han Dynasty and the 21st century, China lost its independence only once – to the Mongol armies of Genghis Khan in 1215 CE.