The best place to start with any story is the beginning. For the Romans, this beginning was Caesar Augustus and his father Julius Caesar. While it is Augustus who has become known as the first emperor of Rome, it was only because of his father that this was made possible. In China, Shihuangdi was the man to unite and begin an imperial China.
These great men both used similar governing tactics to bring peace to war-ravaged areas of their empire. By doing this, they both changed the way governing was done for their empires. While the prolonged peace was welcome by many people, the wealthy aristocrats in both empires disliked this new way of doing things. This is what eventually led to the assassination of Caesar, as well as three attempts on the life of Shihuangdi.
Currency was looked at differently between both ancient cultures. Rome was a much more monetized culture. In China, they produced only bronze coins while the Romans used bronze, silver, and gold to produce their coinage. Roman coins were used for propaganda purposes as much as monetary. It was not uncommon for Roman coins to be melted down and reminted with current emperor images or messages.
Differences in writing were also prevalent. While it was the Chinese who invented paper, it would be a while before it would be widely used. Until then, it was much more common to use strips of wood or bamboo as writing material. The Romans had papyrus and parchment, but both were expensive so it was wax tablets that were used more commonly.
One striking difference was the amount of public entertainment each culture provided. Romans are famous for their over-the-top entertainment venues and shows. These venues housed a variety of spectacles, including gladiator fights and chariot races. The Chinese also enjoyed public entertainment but on a much more modest level. This entertainment consisted of less violent and grandiose acrobat and juggling acts.
To know ourselves is to know our past. This is why websites like ChinaAndRome.org and other educational organizations are fighting to help the youth of today understand the ways of yesterday.