In this work, we assess several deep learning strategies for hyperspectral pansharpening. First, we present a new dataset with a greater extent than any other in the state of the art. This dataset, collected using the ASI PRISMA satellite, covers about 262200 km2, and its heterogeneity is granted by randomly sampling the Earth's soil. Second, we adapted several state of the art approaches based on deep learning to fit PRISMA hyperspectral data and then assessed, quantitatively and qualitatively, the performance in this new scenario. The investigation has included two settings: Reduced Resolution (RR) to evaluate the techniques in a supervised environment and Full Resolution (FR) for a real-world evaluation. The main purpose is the evaluation of the reconstruction fidelity of the considered methods. In both scenarios, for the sake of completeness, we also included machine-learning-free approaches. From this extensive analysis has emerged that data-driven neural network methods outperform machine-learning-free approaches and adapt better to the task of hyperspectral pansharpening, both in RR and FR protocols.