Adsorption of cell-penetrating peptides (CPPs) at cellular membranes is the first and necessary step for their subsequent translocation across cellular membranes into the cytosol. It has been experimentally shown that CPPs rich in arginine (Arg) amino acid penetrate across phospholipid bilayers more effectively than their lysine (Lys) rich counterparts. In this work, we aim to understand the differences in the first translocation step, adsorption of Arg₉ and Lys₉ peptides at fully hydrated neutral phosphatidylcholine (PC) and phosphatidylethanolamine (PE) lipid bilayers and evaluate in detail the energetics of the process using molecular dynamics (MD) simulations and free energy calculations of adsorption of the single peptide. We show that the adsorption of Arg₉ is energetically feasible, with the free energy of adsorption being ∼−5.0 kcal mol⁻¹ at PC and ∼−5.5 kcal mol⁻¹ at PE bilayers. In contrast, adsorption of Lys₉ is not observed at PC bilayers, and their adsorption at PE bilayers is very weak, being ∼−0.5 kcal mol⁻¹. We show by energy decomposition and analysis of peptide hydration along the membrane that significantly stronger electrostatic interactions of Arg₉ with lipid phosphate groups, together with the greater loss of peptide hydration (and in turn stronger hydrophobic interactions) along the membrane translocation path, are the main driving factors governing the adsorption of Arg-rich peptides at neutral lipid bilayers in contrast to Lys-rich peptides. Finally, we also compare the energetics in lipid/bilayer systems with the density functional theory (DFT) calculations of the corresponding model systems in the continuum water model and reveal the energetic differences in different environments.