We perform a comparative study of HfO ₂ and Ta ₂ O ₅ resistive switching memory (RRAM) devices for their possible application as electronic synapses. By means of electrical characterization and simulations, we link their electrical behavior (digital or analog switching) to the properties and evolution of the conductive filament (CF). More specifically, we identify that bias-polarity-dependent digital switching in HfO ₂ RRAM is primarily related to the creation and rupture of an oxide barrier. Conversely, the modulation of the CF size in Ta ₂ O ₅ RRAM allows bias-polarity-independent analog switching with multiple states. Therefore, when the Ta ₂ O ₅ RRAM is used to implement a synapse in multilayer perceptron neural networks operated by back-propagation algorithms, patterns in handwritten digits can be recognized with high accuracy.