Level set methods and volume of fluid (VOF) methods have been widely used for computing immiscible-fluid flows. While it is well known that these methods have their own advantages, there are few examples that applied both approaches to the same benchmark problems and made a critical comparison of the characteristics from a user’s perspective. The present study is an extension of Ishikawa et al. [J. JSCE A2 76(2) I 439 2020], who compared the ACLS (a level set variant) and CICSAM (a VOF variant) methods mainly in pure advection problems. Here another VOF variant, i.e., the THINC/WLIC method, is added to the comparison. The three methods are implemented with the same Navier-Stokes solver and critically compared in fundamental gas-liquid two-phase flow problems in two dimensions in terms of accuracy and computational cost. In the dam-break benchmark test, where the surface deformation is large and the surface tension effect is negligible, not only the VOF variants but the ACLS method show sufficient mass conservation ability and provide an accurate prediction. In the static/rising bubble problems, the ACLS method accurately represents the surface tension force within the framework of the continuum surface force model. While the VOF variants are found to be less precise, introducing the S-CLSVOF method that efficiently constructs a signed-distance function from the volume fraction field improves the prediction accuracy significantly. As to the computational cost, the ACLS method is the most expensive in pure advection problems. In the two-phase flow computations, however, the cost associated with the flow solver is dominant, and hence there is no significant difference in the total cost.