Two spaceborne instruments share the scientific objective of mapping the global Sea Surface Salinity (SSS). ESA's Soil Moisture and Ocean Salinity (SMOS) and NASA's Aquarius use L-band (1.4 GHz) radiometry to retrieve SSS. We find that SSS retrieved by SMOS is generally lower than SSS retrieved by Aquarius, except for very cold waters where SMOS SSS is higher overall. The spatial distribution of the differences in SSS is similar to the distribution of sea surface temperature. There are several differences in the retrieval algorithm that could explain the observed SSS differences. We assess the impact of the dielectric constant model and the ancillary sea surface salinity used by both missions for calibrating the radiometers and retrieving SSS. The differences in dielectric constant model produce differences in SSS of the order of 0.3 psu and exhibit a dependence on latitude and temperature. We use comparisons with the Argo in situ data to assess the performances of the model in various regions of the globe. Finally, the differences in the ancillary sea surface salinity products used to perform the vicarious calibration of both instruments are relatively small (0.1 psu), but not negligible considering the requirements for spaceborne remote sensing of SSS.