While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. In this study, we performed three-dimensional (3D) and 1D flow simulations coupled to a two-mass model of adult male vocal folds and compared voice production at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were obtained by solving the compressible Navier-Stokes equations using the volume penalization method with the moving vocal fold wall as an immersed boundary. Despite differences in the predicted flow pressure on vocal fold surface between the 1D and 3D flow models, the results showed reasonable agreement in vocal fold vibration patterns and selected voice outcome measures between the 1D and 3D models for the range of left-right asymmetric conditions investigated. This indicates that vocal fold properties play a larger role than the glottal flow in determining the overall pattern of vocal fold vibration and the produced voice, and the 1D flow simplification is sufficient in modeling phonation, at least for the simplified glottal geometry of this study.