This paper presents the comparison of two metaheuristic approaches: Differential Evolution (DE) and Particle Swarm Optimization (PSO) in the training of feed-forward neural network to predict the daily stock prices. Stock market prediction is the act of trying to determine the future value of a company stock or other financial instrument traded on a financial exchange. The successful prediction of a stock's future price could yield significant profit. The feasibility, effectiveness and generic nature of both DE and PSO approaches investigated are exemplarily demonstrated. Comparisons were made between the two approaches in terms of the prediction accuracy and convergence characteristics. The proposed model is based on the study of historical data, technical indicators and the application of Neural Networks trained with DE and PSO algorithms. Results presented in this paper show the potential of both algorithms applications for the decision making in the stock markets, but DE gives better accuracy compared with PSO.