We compare atomistic and two popular coarse-grained (POL- and BMW-MARTINI) models by studying the interaction between a cationic gold nanoparticle functionalized with primary alkane amines and a lipid bilayer that consists of either zwitterionic lipids or a mixture of zwitterionic and anionic lipids. In the atomistic simulations, the nanoparticle does not exhibit any notable affinity to the zwitterionic bilayer but readily binds to the 9:1 zwitter-ionic:anionic bilayer, and nanoparticle adsorption leads to local segregation of anionic lipids and slowing down of their diffusion. At the coarse-grained level, the POL-MARTINI model does not lead to nanoparticle-membrane binding for either bilayer system, while the BMW-MARTINI model leads to nanoparticle binding to both bilayers; with the BMW-MARTINI model, nanoparticle binding leads to much less demixing of zwitterionic and anionic lipids and moderately higher rates of lipid diffusion. Analysis of nanoparticle properties in solution reveals notable discrepancies in the interfacial charge and water distributions at the coarse-grained level that are likely relevant to their limitations in describing binding interactions with other (bio)molecules.