Wind power forecasting is a tool used in the energy industry for a wide range of applications, such as energy trading and the operation of the grid. A set of models known as decomposition-based hybrid models have stood out in recent times due to promising results in terms of performance. As many publications on this matter are found in the literature, a comparison of these models is difficult, because they are tested under different conditions in terms of data, prediction horizon, and time resolution. In this paper, we provide a comparison unifying these parameters using the main decomposition algorithms and a set of artificial neural network-based models for very short-term wind power forecasting (up to 30 min ahead). For this purpose, a case study using data from an Irish wind farm is performed to analyze the models in terms of accuracy and robustness for a variety of wind power generation scenarios.