The neural correlates of decision making have been extensively studied with tasks involving a choice between two alternatives that is guided by visual cues. While a large body of work argues for a role of the lateral intraparietal (LIP) region of cortex in these tasks, this role may be confounded by the interaction between LIP and other regions, including medial temporal (MT) cortex. Here, we describe a simplified linear model of decision making that is adapted to two tasks: a motion discrimination and a categorization task. We show that the distinct contribution of MT and LIP may indeed be confounded in these tasks. In particular, we argue that the motion discrimination task relies on a straightforward visuomotor mapping, which leads to redundant information between MT and LIP. The categorization task requires a more complex mapping between visual information and decision behavior, and therefore does not lead to redundancy between MT and LIP. Going further, the model predicts that noise correlations within LIP should be greater in the categorization compared to the motion discrimination task due to the presence of shared inputs from MT. The impact of these correlations on task performance is examined by analytically deriving error estimates of an optimal linear readout for shared and unique inputs. Taken together, results clarify the contribution of MT and LIP to decision making and help characterize the role of noise correlations in these regions.