The paper presents two systems to recognize five facial expressions (anger, surprise, joy, sadness and neutral) and gives a performance review on them. Both systems are developed on the same facial features extraction process which is histograms of oriented gradients extraction. Vectors of facial features are classified by the systems using the following proposed methods: template matching method based on normalized cross correlation, to find the degree of similarity between inputted images and templates stored in a space of vectors, and supervised learning method of a multi-layer feed-forward neural network. Paper results demonstrate that the adopted methods are efficient, accurate and compete one with other. According to the performance review of these two methods on a three experimental databases (Karolinska Directed Emotional Faces, Cohn-Kanade and Chicago Face Database), normalized cross correlation recognize facial expressions rapidly in high resolutions while neural network is slower but more accurate during classification.