Top-down attention allows people to focus on task-relevant visual information. Is the resulting perceptual boost task-dependent in naturalistic settings? We aim to answer this with a large-scale computational experiment. First, we design a collection of visual tasks, each consisting of classifying images from a chosen task set (subset of ImageNet categories). The nature of a task is determined by which categories are included in the task set. Second, on each task we train an attention-augmented neural network and then compare its accuracy to that of a baseline network. We show that the perceptual boost of attention is stronger with increasing task-set difficulty, weaker with increasing task-set size and weaker with increasing perceptual similarity within a task set.