A data-driven model, in conjunction with economic model predictive control, presents a promising approach to enhance the control of an industrial system with limited development cost. Neural network-based models inherently offer the capacity to identify a wide spectrum of dynamic systems, a pivotal aspect in ensuring a flexible control methodology. However, the training of such neural models requires datasets that are often unattainable in practical scenarios, given that available data is typically confined to the operational data of the system. The literature has shown that linear models are sometimes more relevant in these types of situations, even if they are less flexible. This contribution proposes a comparative study between black-box linear models and neural networkbased models. The objective is to evaluate their relevance when used as part of economic predictive controllers in the context of building temperature regulation. The BOPTEST (Building Optimization Performance Tests) benchmark is used for this purpose. Emphasis is placed on different nonlinear model structures to better understand their influence on the results observed in the literature.