Energy demands and fuel costs are continuously increasing which necessitates either finding new energy resources or improving current energy systems. Multi-generation systems as cogeneration (CHP) and trigeneration (CCHP) are interesting solutions that can enhance energy generation performance and fix some interrelated reliability, safety, and flexibility issues. In this regard, many prime mover technologies are available in which the choice between each is greatly dependent on end-user conditions and preferences. Yet, it is prior to choose whether cogeneration or trigeneration is more suitable. Thus, this paper reviews the main differences between CHP and CCHP systems in most available prime mover technologies, after which a selection table is proposed in order to make appropriate multi-generation system installation choices, depending on specific case study parameters. In general, CHP and CCHP systems yield positive technical and environmental performance impacts.