  We report the results of a direct comparison between different kinetic models
of collisionless plasma turbulence in two spatial dimensions. The models
considered include a first principles fully-kinetic (FK) description, two
widely used reduced models [gyrokinetic (GK) and hybrid-kinetic (HK) with fluid
electrons], and a novel reduced gyrokinetic approach (KREHM). Two different ion
beta ($\beta_i$) regimes are considered: 0.1 and 0.5. For $\beta_i=0.5$, good
agreement between the GK and FK models is found at scales ranging from the ion
to the electron gyroradius, thus providing firm evidence for a kinetic Alfv\'en
cascade scenario. In the same range, the HK model produces shallower spectral
slopes, presumably due to the lack of electron Landau damping. For
$\beta_i=0.1$, a detailed analysis of spectral ratios reveals a slight
disagreement between the GK and FK descriptions at kinetic scales, even though
kinetic Alfv\'en fluctuations likely still play a significant role. The
discrepancy can be traced back to scales above the ion gyroradius, where the FK
and HK results seem to suggest the presence of fast magnetosonic and ion
Bernstein modes in both plasma beta regimes, but with a more notable deviation
from GK in the low-beta case. The identified practical limits and strengths of
reduced-kinetic approximations, compared here against the fully-kinetic model
on a case-by-case basis, may provide valuable insight into the main kinetic
effects at play in turbulent collisionless plasmas, such as the solar wind.
