The development of deep convolutional neural networks (CNNs) has recently led to great successes in computer vision, and CNNs have become de facto computational models of vision. However, a growing body of work suggests that they exhibit critical limitations on tasks beyond image categorization. Here, we study one such fundamental limitation, concerning the judgment of whether two simultaneously presented items are the same or different (SD) compared with a baseline assessment of their spatial relationship (SR). In both human subjects and artificial neural networks, we test the prediction that SD tasks recruit additional cortical mechanisms which underlie critical aspects of visual cognition that are not explained by current computational models. We thus recorded electroencephalography (EEG) signals from human participants engaged in the same tasks as the computational models. Importantly, in humans the two tasks were matched in terms of difficulty by an adaptive psychometric procedure; yet, on top of a modulation of evoked potentials (EPs), our results revealed higher activity in the low β (16–24 Hz) band in the SD compared with the SR conditions. We surmise that these oscillations reflect the crucial involvement of additional mechanisms, such as working memory and attention, which are missing in current feed-forward CNNs.