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Comparisons are presented between a hybrid Vlasov-Maxwell (HVM ) simulation of turbulence in a collisionless plasma and fluid reductions. These includ e Hall- magnetohydrodynamics (HMHD) and Landau fluid (LF) or FLR-Land au fluid (FLR- LF) models that retain pressure anisotropy and low-frequency kin etic effects such as Landau damping and, for the last model, finite Larmor radius (FLR) c orrections. The problem is considered in two space dimensions, when initial conditio ns involve moderate-amplitude perturbations of a homogeneous equilibrium pla sma subject to an out-of-plane magnetic field. LF turns out to provide an accurat e description of the velocity field up to the ion Larmor radius scale, and even to smaller scales for the magnetic field. Compressibility nevertheless appears significant ly larger at the sub-ion scales in the fluid models than in the HVM simulation. High freque ncy ki- netic effects, such as cyclotron resonances, not retained by fluid descriptions, could be at the origin of this discrepancy. A significant temperature anisotr opy is generated, with a bias towards the perpendicular component, the more intense fluctuations being rather spread out and located in a broad vicinity of current sheets . Non-gyrotropic pressure tensor components are measured and their fluctuation s are shown to reach a significant fraction of the total pressure fluctuation, with inten se regions closely correlated with current sheets.