The responses of Earth’s and Mars’ thermospheric densities to quasi-periodic solar rotation variations in flux were measured contemporaneously by the MAVEN, GOES, and Swarm-C satellites. While large solar rotation variability is found in both planetary thermospheres, correlation analyses performed on 6+ years of data reveal that, independently of flux level, Earth's daytime density response is about 10-50% larger than Mars' at a similar density level. Important altitude dependencies in the sensitivities are found in the Martian thermosphere, while the terrestrial thermosphere is shown to exhibit only small (±5%) day/night and latitude variations in the response. Detailed analyses focused on correlative periods in 2015-2016 and 2020 indicate important solar cycle effects in the sensitivities of both planetary thermospheres, with increased slopes with low solar flux. These results provide important new insights into processes relevant to the interpretation of the sources of short-term density variability in Mars’ and Earth's thermospheres associated with solar drivers and point to the need for targeted modeling efforts along with dedicated data analyses to help resolve current unknowns in thermal balance processes.