In recent years artificial neural networks achieved performance close to or better than humans in several domains: tasks that were previously human prerogatives, such as language processing, have witnessed remarkable improvements in state of the art models. One advantage of this technological boost is to facilitate comparison between different neural networks and human performance, in order to deepen our understanding of human cognition. Here, we investigate which neural network architecture (feed-forward vs. recurrent) matches human behavior in artificial grammar learning, a crucial aspect of language acquisition. Prior experimental studies proved that artificial grammars can be learnt by human subjects after little exposure and often without explicit knowledge of the underlying rules. We tested four grammars with different complexity levels both in humans and in feedforward and recurrent networks. Our results show that both architectures can 'learn' (via error back-propagation) the grammars after the same number of training sequences as humans do, but recurrent networks perform closer to humans than feedforward ones, irrespective of the grammar complexity level. Moreover, similar to visual processing, in which feedforward and recurrent architectures have been related to unconscious and conscious processes, our results suggest that explicit learning is best modeled by recurrent architectures, whereas feedforward networks better capture the dynamics involved in implicit learning.