Corals require efficient heat and mass transfer with the overlying water column to support key biological processes, such as nutrient uptake and mitigation of thermal stress. Transfer rates are primarily determined by flow conditions, coral morphology and the physics of the resulting fluid-structure interaction, yet the relationship among these parameters is poorly understood especially for wave-dominated coral habitats. To investigate the interactive effects of these factors on fluxes of heat and mass, we measure hydrodynamic characteristics in situ over three distinct surface morphologies of massive stony corals in a Panamanian reef. Additionally, we implement a numerical model of flow and thermal transport for both current and wave conditions past a natural coral surface, as well as past three simplified coral morphologies with varying ratios of surface roughness spacing-to-height. We find oscillatory flow enhances rates of heat and mass transfer by 1.2-2.0× compared with unidirectional flow. Additionally, increases in Reynolds number and in surface roughness ratio produce up to a 3.3× and a 2.0× enhancement, respectively. However, as waves begin to dominate the flow regime relative to unidirectional currents, the underlying physical mechanisms mediating transfer rates shift from predominantly turbulence-driven to greater control by inertial accelerations, resulting in larger heat and mass transfer for small surface roughness ratios. We show that for rough corals in wave-dominated flows, novel trade-off dynamics for heat and mass transfer exist between broadly spaced roughness that enhances turbulence production versus narrowly spaced roughness that produces greater surface area. These findings have important implications for differential survivorship during heat-induced coral bleaching, particularly as thermal stress events become increasingly common with global climate change.