Stiff or semi-flexible polymers have the potential to generate a diverse family of network-based materials. Such materials differ significantly in structure from those seen in polymeric systems formed from molecules approximated by the freely jointed chain. The solution behavior is well known for specific biological examples such as F-actin, microtubules, DNA etc. under the influence of cross-linking proteins or specific ionic conditions. However, a general picture of phase behavior and the range of accessible structures as a function of flexibility, length, attractive potential, and concentration has not yet emerged as these parameters are often difficult to tune experimentally. Here we show an approach to this problem by modeling filament assembly under the influence of a modified Lennard-Jones potential, and a rich variety of network structures, as seen in biological and synthetic examples, are generated. Our results reveal that previously observed networks of bundles seen in F-actin systems are not unique to certain cross-linkers but occupy a tunable position in the phase diagram. Further modification of filament parameters allows the generation of hierarchically structured networks not seen in flexible polymer systems. Our coarse-grained model, inspired by models of F-actin networks with explicit cross-linkers, greatly expands the accessible parameter space. Approximating the effect of crosslinkers by a Lennard-Jones like potential allows for a more tunable representation of filament attraction and binding. The network phases are observed and diagrammed, showing transitions between distinct structures. Morphological properties of the networks are quantitatively examined using connectivity analysis, radial pair distribution functions and a scaling analysis. Detailing the effects of semi-flexible filament parameters on structure and connectivity in this way provides a roadmap for the design of highly tunable hierarchical networks and aids in the discovery of previously unseen structures for novel bioinspired materials.