With the advent of powerful convolutional neural networks (CNNs), recent studies have extended early applications of neural networks to imaging tasks thus making CNNs a potential new tool for assessing medical image quality. Here, we compare a CNN to model observers in a search task for two possible signals (a simulated mass and a smaller simulated micro-calcification) embedded in filtered noise and single slices of Digital Breast Tomosynthesis (DBT) virtual phantoms. For the case of the filtered noise, we show how a CNN can approximate the ideal observer for a search task, achieving a statistical efficiency of 0.77 for the microcalcification and 0.78 for the mass. For search in single slices of DBT phantoms, we show that a Channelized Hotelling Observer (CHO) performance is affected detrimentally by false positives related to anatomic variations and results in detection accuracy below human observer performance. In contrast, the CNN learns to identify and discount the backgrounds, and achieves performance comparable to that of human observer and superior to model observers (Proportion Correct for the microcalcification: CNN = 0.96; Humans = 0.98; CHO = 0.84; Proportion Correct for the mass: CNN = 0.98; Humans = 0.83; CHO = 0.51). Together, our results provide an important evaluation of CNN methods by benchmarking their performance against human and model observers in complex search tasks.