Although rotational seismology has progressed in recent decades, the links between rotational ground motion and site soil conditions are poorly documented. New experiments were performed on Kefalonia Island (Greece) following two large earthquakes (M W = 6.0, M W = 5.9) in early 2014 on two well-characterized sites (soft soil, V S30 ~ 250 m/s; rock, V S30 ~ 830 m/s, V S30 being harmonic average shear-wave velocity between 0 and 30 m depth). These earthquakes led to large six-component (three translations and three rotations) datasets of hundreds of well-recorded events. The relationship between peak translational acceleration versus peak rotational velocity is found sensitive to the site conditions mainly for the rotation around the vertical axis (torsion; dominated by Love waves): the stiffer the soil, the lower the torsion, for a given level of translational acceleration. For rotation around the horizontal axes (rocking; dominated by Rayleigh waves), this acceleration/rotation relationship exhibits much weaker differences between soft and rock sites. Using only the rotation sensor, an estimate of the Love-to-Rayleigh energy ratios could be carried out and provided the same results as previous studies that have analyzed the Love- and Rayleigh-wave energy proportions using data from translational arrays deployed at the same two sites. The coupling of translational and rotational measurements appears to be useful, not only for direct applications of engineering seismology, but also to investigate the composition of the wavefield, while avoiding deployment of dense arrays. The availability of new, low-noise rotation sensors that are easy to deploy in the field is of great interest and should extend the use of rotation sensors and expand their possible applications.