Solar collectors are key components that allow the exploitation of solar radiation in sustainable applications such as solar cooling systems. However, the selection criteria of the suitable technology of solar collector are still ambiguous. This paper presents a comprehensive investigation of absorption and adsorption cooling systems powered by different solar collectors, namely flat plate collector, evacuated-tube collector, compound parabolic collector, parabolic trough collector, photovoltaic thermal collector and a new configuration of concentrating photovoltaic thermal collector, for air-conditioning application in a residential building. Thus, the impact of each solar collector on thermal, economic and environmental performances of the solar cooling systems is quantified to identify the most cost-effective and eco-friendly system, under three different climate conditions. The performance results showed that the proposed concentrating photovoltaic thermal collector performed the best for absorption cooling system with a solar coefficient of performance of 0.449, 0.428 and 0.414 in Marrakesh, Barcelona and Oslo cities, characterized by hot arid, warm temperate and boreal climates, respectively, and for the adsorption cooling system as well in Oslo city with a solar coefficient of performance of 0.351, while photovoltaic thermal collector exhibited the best performance for adsorption cooling system in Marrakesh and Barcelona cities with a solar coefficient of performance of 0.397 and 0.386, respectively. Furthermore, the economic findings revealed that the photovoltaic thermal collector is the most cost-effective one for absorption/adsorption systems, with levelized cost of cooling in the order of €0.106/0.111, €0.137/0.142 and €0.287/0.313 per kWh, and discounted payback period of 11.25/11.43, 15.23/14.94 and 24/25.63 years in Marrakesh, Barcelona and Oslo cities, respectively. Besides, evacuated-tube collector is found to be the most environmentally-friendly collector, since it allows reducing greenhouse gases emissions especially in boreal climate with a life cycle climate performance of 5.86/5.99 tCO2 for absorption/adsorption systems.