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The study aims to explore wavelet applications for analyzing nonlinear boundary value problems. Although several wavelet methods are reviewed in the literature, a comparative study of their strengths and limitations has found only a few attempts. This study bridges the gap between two wavelet-based numerical methods, namely, higher order Daubechies waveletbased Galerkin method and Haar wavelet collocation method, by conducting a comparative study. Nonlinear boundary value problems arising in mathematical physics are solved using both schemes, followed by the computation of optimal error estimates. Furthermore, the advantages offered by the Haar wavelet collocation method over the wavelet-Galerkin method and the rate of convergence are also discussed in detail. [ABSTRACT FROM AUTHOR]