Using plane-strain compression experiments this article elucidates the competing mechanisms of shear band formation (spatially distributed narrow, sharp shear bands: NBs versus localized composite shear bands: CBs) in heterogeneous elastoplastic solids as a function of pre-existing weak flaws. Homogeneous representative models without pre-existing flaws produced uniformly distributed, closely spaced NBs in conjugate sets, symmetrically oriented at angles of 41°-44° to the compression axis. Heterogeneous models, in contrast, formed CBs at an angle of 46°-49°, localized preferentially against the flaws, leaving the host almost free from any band growth. With increasing finite strains (6% to 18%) the CBs grew to a characteristic wide-band structure, typically comprising a core of densely packed band-parallel sharp secondary bands, flanked by linear regions (transition zone) of closely spaced, across-band NBs. We provide a band density analysis to show the distinctive shear-band characteristics for the homogeneous and heterogeneous models. This study also investigates the effects of global strain-rate (ε′) on the band localization mechanism in heterogeneous solids. Decreasing ε′ (3 x 10-5 sec-1 to 2 x 10-5 sec-1) is found to transform the composite bands into well-defined homogeneous shear bands (HBs) that contain a homogeneously sheared core, flanked by narrow zones of gradational shear into completely unstrained walls. We support our experimental findings with numerical model simulations in the framework of visco-elasto-plastic rheology. The article finally presents a set of geological examples to discuss various types of shear band structures in the light of heterogeneous model findings.