Primates—including humans—can typically recognize objects in visual images at a glance even in the face of naturally occurring identity-preserving image transformations (e.g. changes in viewpoint). A primary neuroscience goal is to uncover neuron-level mechanistic models that quantitatively explain this behavior by predicting primate performance for each and every image. Here, we applied this stringent behavioral prediction test to the leading mechanistic models of primate vision (specifically, deep, convolutional, artificial neural networks; ANNs) by directly comparing their behavioral signatures against those of humans and rhesus macaque monkeys. Using high-throughput data collection systems for human and monkey psychophysics, we collected over one million behavioral trials for 2400 images over 276 binary object discrimination tasks. Consistent with previous work, we observed that state-of-the-art deep, feed-forward convolutional ANNs trained for visual categorization (termed DCNNIC models) accurately predicted primate patterns of object-level confusion. However, when we examined behavioral performance for individual images within each object discrimination task, we found that all tested DCNNIC models were significantly non-predictive of primate performance, and that this prediction failure was not accounted for by simple image attributes, nor rescued by simple model modifications. These results show that current DCNNIC models cannot account for the image-level behavioral patterns of primates, and that new ANN models are needed to more precisely capture the neural mechanisms underlying primate object vision. To this end, large-scale, high-resolution primate behavioral benchmarks—such as those obtained here—could serve as direct guides for discovering such models.