In this work we present a comparison between the two liquid scintillators BC-501A and BC-537 in terms of their performance regarding the pulse-shape discrimination between neutrons and γ rays. Special emphasis is put on the application of artificial neural networks. The results show a systematically higher γ-ray rejection ratio for BC-501A compared to BC-537 applying the commonly used charge comparison method. Using the artificial neural network approach the discrimination quality was improved to more than 95% rejection efficiency of γ rays over the energy range 150 to 1000 keV for both BC-501A and BC-537. However, due to the larger light output of BC-501A compared to BC-537, neutrons could be identified in BC-501A using artificial neural networks down to a recoil proton energy of 800 keV compared to a recoil deuteron energy of 1200 keV for BC-537. We conclude that using artificial neural networks it is possible to obtain the same γ-ray rejection quality from both BC-501A and BC-537 for neutrons above a low-energy threshold. This threshold is, however, lower for BC-501A, which is important for nuclear structure spectroscopy experiments of rare reaction channels where low-energy interactions dominates.