Nonlinear steady-state seepage analysis often suffers from convergence difficulties due to strongly nonlinear hydraulic constitutive models and their sensitivity to material parameters. While Picard- and Newton-type methods are widely used in practice, their convergence behavior and computational performance depend on the degree of material nonlinearity and the adopted step-length control strategy. This study examines material-model sensitivity in nonlinear steady-state seepage by comparing Picard, full Newton, and relaxed Newton formulations combined with multiple step-length control schemes. A consistent numerical setup is adopted to examine the effects of solver type, step-length control, and hydraulic material nonlinearity. Multiple hydraulic constitutive models with different degrees of nonlinearity are considered, and all problems are solved under consistent formulations and convergence criteria. The analysis focuses on convergence trends and iteration behavior across combinations of material models and step-length control strategies. From a general perspective, Picard iterations may exhibit relatively stable behavior under strongly nonlinear conditions, potentially at the expense of increased iteration counts and computational cost. Newton-type methods can provide rapid convergence when stability is maintained, but their robustness under strong nonlinearity is often influenced by the selection and tuning of relaxation or backtracking schemes. Step-length control is therefore expected to play a key role in shaping the convergence behavior of Newton-based methods, with effectiveness varying by hydraulic constitutive model. By clarifying the interplay between hydraulic material models, nonlinear solution strategies, and step-length control, this study aims to provide general insights into solver behavior and to support informed solver selection and stabilization for reliable nonlinear seepage analysis in engineering applications.