Identifying subjects with epileptic seizures or psychogenic non-epileptic seizures from healthy subjects via interictal EEG analysis can be a very challenging issue. Indeed, at visual inspection, EEG can be normal in both cases. This paper proposes an automatic diagnosis approach based on deep learning to differentiate three classes: subjects with epileptic seizures (ES), subjects with non-epileptic psychogenic seizures (PNES) and control subjects (CS), analyzed by non-invasive low-density interictal scalp EEG recordings. The EEGs of 42 patients with new-onset ES, 42 patients with PNES video recorded and 19 patients with CS all with normal interictal EEG on visual inspection, were analyzed in the study; none of them was taking psychotropic drugs before registration. The processing pipeline applies empirical mode decomposition (EMD) to 5s EEG segments of 19 channels in order to extract enhanced features learned automatically from the customized convolutional neural network (CNN). The resulting CNN has been shown to perform well during classification, with an accuracy of 85.7%; these results encourage the use of deep processing systems to assist clinicians in difficult clinical settings.