We investigate full-field petroleum production forecasting using machine learning. A data-driven proxy model that predicts field-scale production under various operational scenarios is proposed. It offers an alternative to time-consuming numerical simulators for assisting operational oilfield management decisions like designing waterflooding schedules and quantifying production loss caused by schedule delays. Its accuracy is validated with real-world datasets. Beyond its practical application, we leverage the proposed workflow to conduct a systematic comparison of several machine learning and deep learning algorithms using four datasets and three forecast horizons. Such critical and systematic analysis is long overdue and seems to be extremely rare in related works, which consistently favor increasingly intricate neural networks, despite the presence of relatively limited and sparse datasets, low-dimensional input variables and the existence of well-defined physical laws to guide input selection. Our comparative study suggests deep learning is an overkill in the context of full-field production forecasts, without any tangible benefits in terms of accuracy. Kernel-based models consistently outperform neural-based architectures in this multi-dimensional analysis. In addition, we find evidence that algorithmic generalization in the full-field context seems to be more influenced by the spatial density of production data than by dataset size. The data-driven proxy model and the investigative findings of this work can help engineers apply machine learning to petroleum production forecasting. On a broader scale, our results endorse the Green AI paradigm, which advocates for the use of compact architectures that deliver good accuracy with a low computational cost.