Context. The mechanism behind the heating of the solar chromosphere remains unclear. Friction between neutrals and charges is expected to contribute to plasma heating in a partially ionised plasma (PIP). Aims. We aim to study the efficiency of the frictional heating mechanism in partially ionised plasmas by comparing a single-fluid model (1F) using ambipolar diffusion with a two-fluid model (2F) that incorporates elastic collision terms. Methods. We used the MANCHA-2F code to solve the equations for both models numerically. The simulations involved the vertical propagation of fast magneto-acoustic waves from the top of the photosphere through the chromosphere. The model atmosphere was vertically stratified, including a horizontal, homogeneous magnetic field. We also applied linear theory to supplement the numerical results. Finally, we looked at the assumptions of the 1F model to find out what causes the discrepancies among the models. Results. The results show that the temperature increase for the 1F model is slightly higher than for the 2F model, especially with long-period waves. The wave energy flux indicates that in the 2F model, the wave is transporting less energy upwards. From linear theory, we find that the wave in the 2F model loses more energy than in the 1F model in the deep layers, but the opposite effect occurs in the high layers. Conclusions. The efficient dissipation in the 2F model in deep layers reduces the energy flux at high layers, thereby reducing heating, which explains the temperature differences between the models. We attribute those discrepancies to the contribution of pressure forces to the drift velocity and the omission of a term related to the centre of mass frame reference in the 1F energy equation.