  Kinetic-range turbulence in magnetized plasmas and, in particular, in the
context of solar-wind turbulence has been extensively investigated over the
past decades via numerical simulations. Among others, one of the widely adopted
reduced plasma model is the so-called hybrid-kinetic model, where the ions are
fully kinetic and the electrons are treated as a neutralizing (inertial or
massless) fluid. Within the same model, different numerical methods and/or
approaches to turbulence development have been employed. In the present work,
we present a comparison between two-dimensional hybrid-kinetic simulations of
plasma turbulence obtained with two complementary approaches spanning about two
decades in wavenumber - from MHD inertial range to scales well below the ion
gyroradius - with a state-of-the-art accuracy. One approach employs hybrid
particle-in-cell (HPIC) simulations of freely-decaying Alfv\'enic turbulence,
whereas the other consists of Eulerian hybrid Vlasov-Maxwell (HVM) simulations
of turbulence continuously driven with partially-compressible large-scale
fluctuations. Despite the completely different initialization and
injection/drive at large scales, the same properties of turbulent fluctuations
at $k_\perp\rho_i\gtrsim1$ are observed. The system indeed self-consistently
"reprocesses" the turbulent fluctuations while they are cascading towards
smaller and smaller scales, in a way which actually depends on the plasma beta
parameter. Small-scale turbulence has been found to be mainly populated by
kinetic Alfv\'en wave (KAW) fluctuations for $\beta\geq1$, whereas KAW
fluctuations are only sub-dominant for low-$\beta$.
