First, ancient Rome and Han China both shared social views. Male dominance was a big thing for both, as they only cared to produce male offspring and didn't really care much about the women. In Han China it was a bit of a disgrace to produce women offspring; in Rome women were in the same social level as all of the children, everybody under seven-teen years of age. Even-though they both had sort of a sexism society, their paterfamilias were very loyal and respectful. Rome had a lot more slaves then Han China, however they led to an economical downfall in both ancient Rome and Han China.
Secondly, ancient Rome and Han China both shared political views. The political structures of both were based on very well organized bureaucratic systems with strong monarchy sets of succession. These were two of the most dominant empires of Ancient Europe and Asia. They arose from small states,but with lots of discipline and military toughness, took power over small and quarreling neighbors. However Rome's military was much more powerful in all criteria.
Third, ancient Rome and Han China both shared economical views. The basis wealth in these societies was agriculture since this provided some of the items they traded, however Rome mostly exported glass and metal-works while Han China mostly exported silk and bronze tools. Both empires charged taxes to their people with the exception of slaves.