In crowd scenarios, predicting trajectories of pedestrians is a complex and challenging task depending on many external factors. The topology of the scene and the interactions between the pedestrians are just some of them. Due to advancements in data-science and data collection technologies deep learning methods have recently become a research hotspot in numerous domains. Therefore, it is not surprising that more and more researchers apply these methods to predict trajectories of pedestrians. This paper compares these relatively new deep learning algorithms with classical knowledge-based models that are widely used to simulate pedestrian dynamics. It provides a comprehensive literature review of both approaches, explores technical and application oriented differences, and addresses open questions as well as future development directions. Our investigations point out that the pertinence of knowledge-based models to predict local trajectories is nowadays questionable because of the high accuracy of the deep learning algorithms. Nevertheless, the ability of deep-learning algorithms for large-scale simulation and the description of collective dynamics remains to be demonstrated. Furthermore, the comparison shows that the combination of both approaches (the hybrid approach) seems to be promising to overcome disadvantages like the missing explainability of the deep learning approach.