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 centralised or decentralised 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 centralised control scheme. Indeed, it was shown that a decentralised 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, that global predictive control of the wave energy array offered significant benefits over local decentralised control in increasing the average to peak power ratio of power exported to the grid.