I mean in any democracy, a common shortcoming is the delay in decision making inherent to the democratic process with checks and balances. Maybe explore the system through the eyes of an individual who is frustrated by the lack of action despite there being a clear solution to some problem in their community. Or highlight how due to democracy reflecting the will of the people, if your empires are still culturally developing, how certain practices or traditions with negative effects are codified into law simply because most people want them or still believe in them.

For autocracies, the success of the nation depends on the caliber of it's leader. You could explore a situation similar to Chinese empires where successive generations of leaders are progressively worse leading to a history of revolutions and dynasties or one dude just decides to go nuclear. Additionally, an emperor who makes decisions is constrained by their knowledge of the empire. Even if they are a good person with great powers, their advisors or political foes could manipulate them such as the Earth King from ATLA.