This is a very complex question, but they both collapsed due to:
decentralization and government corruption
plagues/ epidemics
high taxes
and invasions
Some differences are that the Chinese empires saw a revival while Rome didn't.
I am going to guess that it would be a loss of memory.
The part of the essay to draw your reader in is your thesis Statement
Reliance on human reason can lead to chaos and destruction
Definitely C which is Russia