Increasing the efficiency of wind power conversion into electricity poses major challenges to researchers and developers of wind turbines, who are striving for new solutions that can ensure better use of local wind potential in terms of both feasibility and affordability. The paper proposes a novel concept of wind systems with counter-rotating wind rotors that can integrate either conventional or counter-rotating electric generators, by means of the same differential planetary speed increaser, aiming at providing a comparative analysis of the energy performance of counter-rotating wind turbines with counter-rotating vs. conventional electric generators. To this end, a generalized analytical model for angular speeds and torques has been developed, which can be customized for both system configurations. Three numerical simulation scenarios have been contrasted: (a) a scenario with identical wind rotors in both systems, (b) a scenario with the secondary wind rotors being identical in the two applications, but different from the primary rotors, and (c) a scenario with different secondary rotors in the two wind turbines. The results have shown that the wind systems with counter-rotating generator are more efficient and have a higher amplification ratio, compared to systems with conventional generators. In addition, the analyzed wind system with a counter-rotating generator displays better energy performance with low values for output power and ratio of input speeds, whereas the wind turbine with a conventional generator proves to be more efficient in the high-value range of the above-mentioned parameters.