  A set of numerical solvers for the linear dispersion relations of the
gyrokinetic, the hybrid-kinetic, and the fully kinetic model is employed to
study the physics of the kinetic Alfv\'en wave and the fast magnetosonic mode
in these models. In particular, we focus on parameters that are relevant for
solar wind oriented applications (using a homogeneous, isotropic background),
which are characterized by wave propagation angles averaging close to 90{\deg}.
It is found that the gyrokinetic model, while lacking high-frequency solutions
and cyclotron effects, faithfully reproduces the fully kinetic Alfv\'en wave
physics close to, and sometimes significantly beyond, the boundaries of its
range of validity. The hybrid-kinetic model, on the other hand, is much more
complete in terms of high-frequency waves, but owing to its simple electron
model it is found to severely underpredict wave damping rates even on ion
spatial scales across a large range of parameters, despite containing full
kinetic ion physics.
