Over the last decade, the Airborne Wind Energy (AWE) innovation has been evolving with the development of several prototypes by various companies/research institutions. AWE crosswind systems may differ in the electricity generation mode, the wing type, the take-off/landing approaches and the control mechanisms, to name a few. Each system has characteristics which enhance their performance regarding key factors of AWE exploration at the expense of penalizing others. Hence, deciding for the most appropriate system in a possible AWE implementation, targeting a certain location, is a difficult and uncertain scenario. This paper presents a Multi-Criteria Decision Analysis (MCDA) approach, using the Fuzzy Analytic Network Process (FANP), aiming to determine, from nine alternatives, the most suitable AWE crosswind system for two distinct exploration sites: on-shore rural and off-shore. The importance of key selection criteria for AWE is presented and discussed, alternatives in each criterion are evaluated and compared and, finally, a prioritization of both alternatives and criteria is obtained. The FANP methodology indicates rigid wing pumping-cycle systems with horizontal take-off as the most suitable solution for both investigated sites, revealing Aerodynamic Performance, Mass-to-Area Ratio and Controlability as the most relevant factors in the decision.