We compare dewetting characteristics of a thin nonwetting solid film in the absence of stress, for two models of a wetting potential: the exponential and the algebraic. The exponential model is a one-parameter (r) model, and the algebraic model is a two-parameter (r, m) model, where r is the ratio of the characteristic wetting length to the height of the unperturbed film, and m is the exponent of h (film height) in a smooth function that interpolates the system's surface energy above and below the film-substrate interface at z = 0. The exponential model gives monotonically decreasing (with h) wetting chemical potential, while this 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 energy anisotropies demonstrate that for any m the film is less prone to dewetting when it is governed by the algebraic model. Quasiequilibrium states similar to the 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.