This question is much too broad to be answered to any level of satisfaction here. To show you how ridiculous it is, they are similar in that they both are empires, and different in that Rome lasted a fraction of China's imperial history (if one considers that broad stretch of time inclusive of the greater "Chinese Empire").

This sounds like it might have come from a "compare and constrast" homework question. Why don't you simply ask your friend if he's the one who made the claim?