Range-separated hybrid (RSH) functionals have been recently used to overcome the tendency of traditional density functional theory (DFT) calculations to overestimate the conductance of molecular junctions. Non-equilibrium conditions are addressed following non-equilibrium Green's function (NEGF) formulation with RSH functionals to study negative differential resistance (NDR) in molecular junctions of oligo phenylene ethylene derivatives linking gold electrodes. It is shown that the RSH-NEGF calculations indicate NDR onset bias that agrees well with measured trends, associate NDR to orbital localization at the drain contact, and analyze the role of junction asymmetry in NDR. The RSH-NEGF results are also compared with alternative DFT-NEGF combinations to highlight the importance of basing the computational study on a functional that achieves physically significant frontier orbitals. Finally, the effects of thermally accessible molecular fluctuations to enhance the NDR conductance drop are also discussed.