Literature compares DC-DC converters with Si and SiC power semiconductors without optimum switching frequency in terms of efficiency, volume, and costs for the respective application and operating point. Typical switching frequencies, such as 25 kHz for Si-IGBTs and 100 kHz for SiC-MOSFETs, are chosen with unconditional statements. A design with optimum switching frequency is crucial for a meaningful conclusion about the best-suited semiconductor technology for the respective application. This paper uses a novel iterative design procedure to determine the optimum switching frequency considering a trade-off between efficiency, volume, and costs for bidirectional DC-DC converters based on Si-IGBTs and SiC-MOSFETs with ferrite cores. Due to the importance of fuel cell hybrid vehicles as the long-term alternative to conventional vehicles, the application analyzed is the bidirectional DC-DC converter connecting the traction battery to the DC-bus. Both converters are evaluated and compared in the simulation environment PSIM, and their parameters are according to available fuel cell hybrid vehicles on the market. This paper proves in PSIM that the optimum switching frequency in both cases is below the standard values. Furthermore, it presents that Si-IGBTs have efficiency losses of less than 2 % for the operating point of interest than SiC-MOSFETs, reducing semiconductor costs by 68 % while increasing core volume by 344 %.