The linkage of neighboring multi-energy microgrids may overcome the disadvantage of one single microgrid since the surplus/deficient energy can meet internal balance and realize self-satisfaction. In order to realize successful cooperation of such a complicated energy system, optimal trading strategy and reasonable trading price among all entities are important. In this study, a bi-level optimization model combined of two trading modes is proposed under different scenarios: an intermediary agent-based trading mode where the intermediary agent acts as an intermediate operator, as well as a direct trading mode without intermediary agent. The Stackelberg game theory-based method and the supply/demand ratio method are used for price determination, respectively. In addition, the integrated demand response is also considered in this study. As an illustrative example, a comparative study is implemented in a neighboring energy cluster combing three park-level multi-energy microgrids. The results show that, compared with the situation that each multi-energy microgrid acts alone, a cluster obviously increases total benefits, which may contribute to the development of tailored policy instruments. In addition, although direct trading among multi-energy microgrids enjoys higher benefits, its self-sufficient ability is lower than the situation considering intermediary agent, which may help policymakers to predict the merits and demerits associated with different energy trading modes among multi-energy microgrids in a more accurate way.