  A long-lasting debate in space plasma physics concerns the nature of
subproton-scale fluctuations in solar wind (SW) turbulence. Over the past
decade, a series of theoretical and observational studies were presented in
favor of either kinetic Alfv\'en wave (KAW) or whistler turbulence. Here, we
investigate numerically the nature of the subproton-scale turbulent cascade for
typical SW parameters by means of unprecedented high-resolution simulations of
forced hybrid-kinetic turbulence in two real-space and three velocity-space
dimensions. Our analysis suggests that small-scale turbulence in this model is
dominated by KAWs at $\beta\gtrsim1$ and by magnetosonic/whistler fluctuations
at lower $\beta$. The spectral properties of the turbulence appear to be in
good agreement with theoretical predictions. A tentative interpretation of this
result in terms of relative changes in the damping rates of the different waves
is also presented. Overall, the results raise interesting new questions about
the properties and variability of subproton-scale turbulence in the SW,
including its possible dependence on the plasma $\beta$, and call for detailed
and extensive parametric explorations of driven kinetic turbulence in three
dimensions.
