We compare dewetting characteristics of a thin nonwetting solid film in theabsence of stress, fortwo models of a wetting potential: the exponential and the algebraic.The exponential model is a one-parameter (r) model, and the algebraic model isa two-parameter (r, m)model, where r is the ratio of the characteristic wetting length to the heightof the unperturbed film,and m is the exponent of h (film height) in a smooth function thatinterpolates the system's surfaceenergy above and below the film-substrate interface at z = 0. The exponentialmodelgives monotonically decreasing (with h) wetting chemical potential, whilethis dependence is monotonic only for the m = 1 case of the algebraic model.Linear stability analysis of the planar equilibrium surface is performed.Simulations of the surface dynamics in the strongly nonlinear regime(large deviations from the planar equilibrium) and for large surface energyanisotropies demonstrate that for any m the film is less prone to dewettingwhen it is governed by the algebraic model. Quasiequilibrium states similar tothe one found in the exponential model [M. Khenner, Phys. Rev. B, 77 (2008), 245445.] exist in the algebraic model as well, and the film morphologies are similar.