There are some aspects that are the same, mostly owing to geography and demography (China is still China whether red or otherwise), as well as plain old sentiment. Mao must have felt like the emperor of a new dynasty when he gave that speech in Beijing in 1949 as his forces were sweeping aside the KMT armies. So many of the levers of power are going to function in classic imperial fashion. You're going to have the typical Chinese political features of top-down directives, heavy reliance on informal "guanxi" connections and factional interests in tandem to rule of law, and so on, things that have been around since at least the time of the First Emperor.
What people don't get, or ignore, is that there are massive differences between communist China, republican China, HK/Taiwanese China, and imperial China in its various iterations, despite the levers of power functioning rather similarly in all cases on account of the people themselves being Chinese. The differences arise from the ideology and values espoused by different regimes.
The CCP at its core is not content with just running a country. Its ideological roots are in revolutionary struggle and mass mobilization with an elite vanguard at the helm. Whether it uses planned economics or market economics, the underlying political agenda is the same: to have the CCP maintain control over society, gain greater control over society, and expand its control beyond what it already controls. The Party is structured in such a way that incentivizes its leaders to continue pursuing its Marxist-Leninist program of power maximization. Pretty much every social group in China has at one point or another become a direct target of the CCP's political campaigns: religions, businessmen, landowners, peasants, the Party bureaucracy, students, academics, cultural elites, ethnic minorities.
Compare this with various imperial dynasties which were more interested in maintaining the authority of the imperial family, coping with barbarian invaders or natural disasters, or finding the best spiritual-philosophical system to keep elite society in harmony. Or the republican system's Three Principles of the People, which mixed the European ideal of a national welfare state with American concepts of representative government and liberty. Despite several decades of military dictatorship, the KMT continued espousing these principles, rather than the CCP's class struggle, and eventually let Taiwan transition to the democracy they were supposed to have in the first place. In Hong Kong, they had no democracy, but enjoy many rights under the robust British legal system.
If you look at these systems, I'm sure you can find aspects of imperial rule and traditional social hierarchy in all of them because they are all Chinese. But the outcomes of each were totally different.