An opportunity for increasing the parabolic solar power plant efficiency is substituting the actual subcritical Rankine power cycles with the innovative s-CO2 Brayton cycles. In this paper, three configurations are assessed: the recompression cycle (RC), the partial cooling with recompression cycle (PCRC), and the recompression with main compression intercooling cycle (RCMCI), with one reheating stage. The thermodynamic parameters are optimized with three algorithms: SUBPLEX, UOBYQA, and NEWUOA, and the results validated with thermoflow Software. The parabolic troughs and linear Fresnel solar collectors are studied with different heat transfer fluids (HTFs): Solar Salt, HITEC XL, Therminol-VP1, Syltherm 800, and Therminol 75. The dual-loop solar field (SF), combining thermal oil and molten salt (MS) in the same solar plant, is also analyzed. The plant power output and plant energy efficiency are translated into SF aperture area and cost at design point. From the point of view of the plant efficiency and SF cost, the PTC and LF solar collector with Solar Salt as HTF coupled to a s-CO2 Brayton RCMCI cycle is selected as the optimum design solution and compared with the actual PTC Rankine solar plant performance at design point. The total recuperator conductance (UA) plays an important role in optimizing the plant performance, limited by the minimum heat exchangers (HX) pinch point. The UA increment could compensate the HX pressure drop and the compressor inlet temperature (CIT) increment, both impacting very negatively in the s-CO2 plant performance.