I think the fundamental difference is what people were fighting

Americans were fighting against ideas, slavery in this case. The war ended when both sides accepted the same conclusion.

Chinese have always  been fighting against people, one group against another. For Chinese, it is never about the ideas or beliefs, it is all about personal interests. Since there is always winners and losers, the war never ends. In a way, "文革" or other form of revolution will occur periodically as the internal pressure reaches to the critical threshold. In fact  China has stuck in this destructive cycles for the past 2000 years. Honestly, I don't see any solution within Chinese system, political and cultural.