The failure of adhesion between two polymers is a complex phenomenon involving bulk dissipation (i.e., shear yielding, cavitation and crazing), surface adhesion (through Van der Waals interactions) and connector chain pull-out. This article is concerned with a coarse-grained molecular dynamics (MD) study of the competition between physical mechanisms in determining the overall work of separation. A model is presented that incorporates both connector pull-out and dissipation in two adjacent glassy polymers stitched together via connector chains. The contributions to the separation energy from the dissipation in the bulk and at the surface are studied, in dependence of the separation rate at constant temperature and at fixed basic molecular parameters like areal density of the connectors and their chain length. The results are key to future developments of continuum cohesive models for adhesion on polymer surfaces.