Shallow-seismic Rayleigh and Love waves are attractive for geotechnical site investigations. They exhibit a high signal to noise ratio in field data recordings and have a high sensitivity to the S-wave velocity, an important lithological and geotechnical parameter to characterize the very shallow subsurface. In this work we compare the performance of individual full waveform inversion (FWI) of Rayleigh or Love waves and explore the benefits of a simultaneous joint inversion of both types of surfaces waves. The analysis shows that the true S-wave velocity model could be reconstructed by both the individual waveform inversions and the joint inversion of both wave types. The FWI of Rayleigh waves suffers from artifacts below the source positions. These artifacts also appear in the results of the joint inversion, limiting the resolution of the final S-wave velocity and the final data fit. The individual Love wave FWI does not suffer from source artifacts and thus allows for a smooth convergence and excellent final fit. In our synthetic example the single inversion of Love waves is thus superior to the individual inversion of Rayleigh waves and the joint inversion of Rayleigh and Love waves.