G-rich DNA and RNA sequences can fold into G-quadruplexes (G4s), which are noncanonical nucleic acid structures found across all domains of life. Despite growing evidence of their involvement in key cellular processes, their interactions with biological membranes are generally overlooked. Here, we systematically investigated the interaction of several RNA and DNA G4s with model membranes, exploring the influence of G4 conformation, membrane physical state, and net charge. Using a combination of complementary biophysical tecniques, we demonstrate that the interaction of G4s with membranes is modulated by the physical state of the membrane and depends on the type of nucleic acid as well as on the G4 topology. Notably, RNA G-quadruplexes display binding energetics to zwitterionic membranes that differ markedly from those of DNA G-quadruplexes, revealing distinct thermodynamic signatures indicative of specific, non-electrostatic contributions. Consistently, RNA G4s induce more pronounced membrane perturbations compared with DNA G4s. Moreover, RNA-quaduplexes, but not DNA G-quadruplexes, interact strongly with negatively charged membranes. Taken together, our results show that the interaction between G4s and membranes can be finely tuned and is governed by both nucleic acid type and membrane properties.