Well, China was philosophically and religiously unified. Everything was Confucian. The Taos and Buddhists were in the background, but significant as well. Essentially its very similar to Europe pre-reformation. Or rather pre-degrading the schism. Back then the idea of a United Catholic Empire was not one that seemed too far fetched.
The number of years a Dynasty stays in power changes from Dynasty to Dynasty, and even period to period.
The Three Chinese Dynasties that made China possible:
The Xia (semi-mythical) was about 600 years
The Shang (semi-mythical) was about 700 years
The Zhou (all fact now) was about 800 years
Those defined Early Chinese civilization and were mostly just regime changes and capital changes. Then we get on to the more fuzzy parts. The Zhou, as some of you may know, was divided into dozens of different factions about halfway into it's lifespan. Notably the Spring and Autumn and Warring States period. The Spring and Autumn era saw the rise of a few major powers in China that consumed everyone else. The warring states period was when there were only major powers, and they were only attacking each other. It ended up with the Qing ruling them all.
The Qin lasted roughly 15 years.
Then we get to the Han, The Han was basically Rome. It lasted around 400 years and filled in what most would call "Core China"
After those 400 years the Empire began to fall apart in 180s, but was officially ended in the 220s, long after the nation was carved into three. We get the Three Kingdoms era, a popular topic.
This era of division lasted for 60 years, a bit longer accounting for de facto independent. The Jin would take over China, but the Jin would almost immediately collapse for reasons stated about a page ago. The Jin lasted just 36 years as an independent country. A Chinese state would exist in the south, uniting all sovereign Chinese, for centuries. The Northern and Southern Dynastic period refers to the Northern "Wu Hu" Dynasties and the Southern Chinese Dynasties. So what we would refer to as China was united and pushed down South for over 160 years. So we have a "west falling to Barbarians while the East stays Roman" situation here.
With this in mind I would have to say unity as a small meaningless nation lasted for thousands of years. When it began to spread unification was fleeting, just 400 years. The Tang would reunite it again, but that would be only for 300 years, and it would still not be what we call China. The Song lasted for just a 300 or so years, but only ruled a united China for a few decades. We thank the Mongols for actually giving China it's form and the Qing for finalizing it.
So, for much of it's early history, it's analogs with Rome are pretty spot on.