Using molecular dynamics simulations, we study how chain stiffness affects how glassy polymers deform under applied shear. Loosely entangled systems composed of flexible chains exhibit strong shear banding and subsequent strain softening whereas tightly entangled systems composed of semiflexible chains exhibit neither of these. For all systems, inflection points in stress-strain curves correspond to the onset of chain scission, but nonlinear strain hardening continues up to much larger strains. Tightly entangled systems build up considerable elastic energy before fracturing via chain scission. This causes their plastic flow to be far more heterogeneous, and they ultimately fail along significantly sharper fracture planes than their loosely entangled counterparts, which fail via chain pullout. We quantify these differences using modern plasticity metrics and relate them to chain-stiffness- dependent differences in segmental packing efficiency and interchain interpenetration. It appears that the additional stress transmission mechanisms provided by the greater covalent bond tensions present in tightly entangled systems act to delocalize strain and promote more homogeneous deformation than is found in loosely entangled systems, but only until chain scission begins.