Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. This behavior is robust over many cell types and many signals, including gradients of extracellular matrix stiffness (durotaxis) and electrical potential (galvanotaxis). Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles in collective chemotaxis. We use a simple mathematical model to understand when this specialization would be advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding while follower cells attempt to follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have much more information than the rest of the cluster, such as in the presence of a sharp transition from one chemical concentration to another. We do find this - but also find that high levels of specialization can be optimal in the opposite limit of a very shallow gradient. This occurs because in a sufficiently shallow gradient, each leader cell has such little information about the gradient direction that - after a sufficient number of leaders are created - adding leader cells adds more noise to the cluster motion than adding a follower cell. There is also an important tradeoff: clusters have to choose between speed in following a gradient and ability to reorient quickly. We find that clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.