Robot navigation through crowds poses a difficult challenge to AI systems, since the methods should result in fast and efficient movement but at the same time are not allowed to compromise safety. Most approaches to date were focused on the combination of pathfinding algorithms with machine learning for pedestrian walking prediction. More recently, reinforcement learning techniques have been proposed in the research literature. In this paper, we perform a comparative evaluation of pathfinding/prediction and reinforcement learning approaches on a crowd movement dataset collected from surveillance videos taken at Grand Central Station in New York. The results demonstrate the strong superiority of state-of-the-art reinforcement learning approaches over pathfinding with state-of-the-art behaviour prediction techniques.