In conventional desiccant and evaporative air-conditioning systems (DEC) employing solid sorptive materials, the regeneration stage is powered by thermal energy. The use of solar energy to assist the regeneration process is obviously a good solution to reduce the primary energy consumption. When looking at the problem from a second law perspective, namely by assessing the overall irreversibility production and the exergy efficiency, this practice is not always sufficient to ensure better performance than a conventional air-conditioning system, especially when high regeneration temperatures are required. In the literature, new concepts for open cycle desiccant cooling systems have been recently proposed, based on the adoption of enthalpy recovery wheels or heating coils working as a desuperheater on the cooling cycle. In this paper a comparative analysis between the conventional DEC systems and these new concepts is carried out both under a first and a second law perspective, in order to understand to what extent the novel thermal cycles may help reducing thermodynamic irrationalities and irreversibilities, taking into account the possibility of assisting regeneration by means of solar energy. The effects of the parasitic consumption of fans and pumps will be accounted for, too. The results will help understanding possible inefficiencies and improvements of the thermal cycles mentioned above, and highlight the fundamental role of the solar energy.