Metallic cellular materials, such as lattices and honeycombs, are of interest in the design of lightweight blast and impact-resistant structures. Additive Manufacturing (AM) has enabled the fabrication of complex metallic cellular materials due to the additional design freedom AM provides. This extends the available design space and scope for performance optimisation. However, there is a need to understand the interactions between: (i) the material architecture, (ii) the AM process parameters, and (iii) the as-built geometry, microstructure and energy-absorbing properties. In this work, we investigate the quasi-static and dynamic behaviour (at 100 m/s tests) of cellular materials manufactured from 316L stainless steel using laser powder bed fusion (LPBF). Four cellular architectures are considered (octet lattice, lattice-walled square honeycomb, origami and square honeycomb). These architectures present different additive manufacturing challenges: they include truss-based and facet-based geometries, with struts and cell walls oriented at a variety of angles to the build plane. Each specimen is manufactured using three different sets of AM process parameters, characterised by laser powers of 50, 125 and 200 W. The exposure time is adjusted to deliver the same total heat input. Cellular materials manufactured with the 125 W process variant match their nominal densities most closely and have the highest strength and energy absorption capacity. Either reducing (50 W) or increasing (200 W) the power leads to a significant increase in porosity, reducing strength and energy absorption. However, we find that changes due to process induced porosity have a smaller influence than those resulting from the choice of cellular architecture. The energy-absorbing performance is more sensitive to optimising the cellular architecture, within the range of AM parameters considered in this investigation.