This work focuses on an array of point absorbers, with linear permanent magnet generators (LPMG) connected to the grid via back-to-back voltage source converters, controlled using economic model predictive control (MPC) that produces optimal electrical power generation. The main contribution of this paper is the comparison of the performance provided by using either a centralized or decentralized MPC scheme. In this study, it is shown how the inclusion of viscosity and system constraints limits the benefits to be obtained by the use of a centralized control scheme. Indeed, it was shown that a decentralized MPC scheme was sufficient for the provision of close to optimum electrical power extraction from the array when there was a reasonable separation between WEC devices. It was shown that the introduction of power constraints, either locally at each device or globally for the entire array, improved the quality of the power exported to the grid. Importantly, it was shown that from the viewpoint of power quality, global predictive control of the wave energy array offered significant benefits over local decentralized control in increasing the average to peak power ratio of power exported to the grid.