The prediction of surface ship response to a far-field underwater explosion (UNDEX) requires the simulation of shock wave propagation in the fluid, cavitation, fluid-structure interaction, and structural response. Effective approaches to model the fluid include cavitating acoustic finite element (CAFE) and cavitating acoustic spectral element (CASE) methods. Although the spectral element method offers the potential for greater accuracy at lower computational cost, it also generates more spurious oscillations around discontinuities which are difficult to avoid in shock-related problems. Thus, the advantage of CASE remains unproven. In this paper, we present a 3D-partitioned FSI framework and investigate the application of CAFE and CASE to a surface ship early-time far-field UNDEX problem to determine which method has the best computational efficiency for this problem. We also associate the accuracy of the structural response with the modeling of cavitation distribution. A further contribution of this work is the examination of different nonmatching mesh information exchange schemes to demonstrate how they affect the structural response and improve the CAFE/CASE methodologies.