For JET L-mode plasmas in low-recycling conditions (electron temperature at the outer strike point, Te,ot≳30eV), SOLPS-ITER simulations agree within the error bars for the experimental profiles at the low-field side (LFS) divertor target. The peak Balmer-α (Dα) emission in the LFS divertor agrees within the error bars of the KS3 filterscope diagnostic, but is approximately 30% lower than the peak value of the KT1 spectrometer. Simulations have been performed with fluid, kinetic, and hybrid models for the neutrals. The large fluid-kinetic discrepancies of more than a factor 2 are successfully corrected by using a hybrid fluid-kinetic approach, for which kinetic atoms are transferred to the fluid population when the local Knudsen number of the atom becomes smaller than a user-defined transition Knudsen number Knt. The hybrid-kinetic discrepancies are limited to a few % for Knt≤100. When increasing the upstream density to high-recycling conditions, at the onset of detachment (Te,ot≈5eV), the simulations predict more than a factor 2 lower peak ion saturation current to the LFS divertor than the experiments. Also the Dα emission is underpredicted with approximately a factor 2. For these high-recycling conditions, the fluid-kinetic discrepancies are limited to maximum 50%, which are again corrected by using the hybrid approach.