Objective. Primarily due to safety concerns, biphasic pulsatile stimulation is the present standard for electrical excitation of neural tissue with a diverse set of applications. While pulses have been shown to be effective to achieve functional outcomes, they have well-known deficits. Due to recent technical advances, galvanic stimulation, delivery of current for extended periods of time (>1s), has re-emerged as an alternative to pulsatile stimulation. Approach. In this paper, we use a winner-take-all decision-making cortical network model to investigate differences between pulsatile and galvanic stimulation in the context of a perceptual decision-making task. Main results. Based on previous work, we hypothesized that galvanic stimulation would produce more spatiotemporally distributed, network-sensitive neural responses, while pulsatile stimulation would produce highly synchronized activation of a limited group of neurons. Our results in-silico support these hypotheses for low-amplitude galvanic stimulation but deviate when galvanic amplitudes are large enough to directly activate or block nearby neurons. Significance. We conclude that with careful parametrization, galvanic stimulation could overcome some limitations of pulsatile stimulation to deliver more naturalistic firing patterns in the group of targeted neurons.