In fluid-structure interaction simulations the meshes at the fluid-structure interface usually do not match, because of the different mesh requirements for the flow and structure. The exchange of data over the discrete interface becomes then far from trivial. In this paper we investigate the difference in accuracy and efficiency between a conservative and a consistent coupling approach. This is done for an analytical test problem as well as a quasi-1D FSI problem, for different coupling methods found in literature. It is found that when the coupling method is based on a weak formulation of the coupling conditions the conservative approach is the best choice. For other coupling methods the consistent approach provides the best accuracy and efficiency, because the conservative approach results in unphysical oscillations in the pressure received by the structure and is therefore not consistent.