In this article, the authors examine two computational approaches that can be used to study the motions of flexible flapping systems. For illustration, a fully coupled interaction of a fluid system with a flapping profile performing harmonic flapping kinematics is studied. In one approach, the fluid model is based on the Navier-Stokes equations for viscous incompressible flow, where all spatio-temporal scales are directly resolved by means of Direct Numerical Simulation (DNS). In the other approach, the fluid model is an inviscid, potential flow model, based on the unsteady vortex lattice method (UVLM). In the UVLM model, the focus is on vortex structures and the fluid dynamics is treated as a problem of vortex kinematics, whereas with the DNS model, the focus is on forming a detailed picture of the flapping physics. The UVLM base approach, although coarse from a modeling standpoint, is computationally inexpensive compared to the DNS based approach. This comparative study is motivated by the hypothesis that flapping related phenomena are primarily determined by vortex interactions and viscous effects play a secondary role, which could mean that a UVLM based approach could be suitable for design purposes and/or constructing a predictive tool. In most of the cases studies in this work, the UVLM base approach produces a good approximation to CL/CD. Apart from comparisons of the aerodynamic loads, comparisons are also made of th features of the system dynamics generated by using the two computational approaches. Limitations of both approaches are also discussed.