As the Marr intro chapter explains so beautifully, there are many levels of analysis in cognitive science and cognitive neuroscience. Units in deep nets are very different from actual neurons, and the backprop methods used to train deep nets have no resemblance to how human brains get wired up. But for the case of object recognition at the level of representation, there are striking similarities between deep nets optimized for invariant object recognition, and parts of the primate brain that carry out this task. See this brilliant and seminal paper: http://www.pnas.org/content/111/23/8619.long