Composite being heterogeneous in nature require homogenization to predict the effective property of composite. This study explores the variational asymptotic method for unit cell homogenization (VAMUCH) and the method of cells (MOC) for multiscale damage modeling in unidirectional composites. These approaches efficiently calculate homogenized properties and relate microscale stresses and strains to macroscale behavior. A comparative analysis of VAMUCH and MOC is performed for three-dimensional damage modeling in laminate composites to predict mechanical response and failure. The strain invariant failure theory (SIFT) is used to determine lamina failure by calculating microstrains and stresses from macro-scale strains under specific loads and boundary conditions. Finite element (FE) formulations for VAMUCH and MOC, along with progressive damage modeling, are implemented in Abaqus using a User Material Subroutine (UMAT) coded in FORTRAN. Damage progression is modeled with the element deletion method, removing damaged integration points to reflect material failure. Results demonstrate the effectiveness of VAMUCH and MOC in linking macro- and microscale phenomena, providing deeper insights into the behavior and failure mechanisms of unidirectional composites.