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Energy supply in an economic and environmentally friendly configuration is a major challenge for urban energy systems. This paper presents two multi-objective models for the design of Distributed Energy Systems (DES) for satisfying local needs in heating, cooling and electricity. DES can be used to promote energy efficiency and reduce carbon emissions which is crucial to tackle climate change. A multi-objective MILP framework is presented, comparing two main methodologies of designing DES using Total Annual Cost (TAC) and carbon emissions as objective functions. The first one, namely "Method A", which performs a simultaneous sizing and the second one, namely "Method B", in which technologies and their respective capacity are predefined. Furthermore, three scenarios regarding the available technologies are developed to assess DES for both methods and a case study is carried out. Results show that in both methods Scenario 3 (a DES coupled with district heating network, microgrid and storage technologies) has the best performance. In terms of comparison between the two methods, "Method A" provides better solutions in terms of cost and emissions as it has more degrees of freedom. Structure, design and operational results are presented and discussed analytically, as well as the possibility of comparing the two methods for a more detailed design.