Polymeric synthetic mimics of antimicrobial peptides (SMAMPs) have recently demonstrated similar antimicrobial activity as natural antimicrobial peptides (AMPs) from innate immunity. This is surprising, since polymeric SMAMPs are heterogeneous in terms of chemical structure (random sequence) and conformation (random coil), in contrast to defined amino acid sequence and intrinsic secondary structure. To understand this better, we compare AMPs with a 'minimal' mimic, a well characterized family of polydisperse cationic methacrylate-based random copolymer SMAMPs. Specifically, we focus on a comparison between the quantifiable membrane curvature generating capacity, charge density, and hydrophobicity of the polymeric SMAMPs and AMPs. Synchrotron small angle x-ray scattering (SAXS) results indicate that typical AMPs and these methacrylate SMAMPs generate similar amounts of membrane negative Gaussian curvature (NGC), which is topologically necessary for a variety of membrane-destabilizing processes. Moreover, the curvature generating ability of SMAMPs is more tolerant of changes in the lipid composition than that of natural AMPs with similar chemical groups, consistent with the lower specificity of SMAMPs. We find that, although the amount of NGC generated by these SMAMPs and AMPs are similar, the SMAMPs require significantly higher levels of hydrophobicity and cationic charge to achieve the same level of membrane deformation. We propose an explanation for these differences, which has implications for new synthetic strategies aimed at improved mimesis of AMPs.