Organic electrochemical transistors (OECTs) are attracting a great deal of interest for biosensing and bioelectronics applications. However, their device physics is not yet well-understood. In this paper, we focus on the effect of the gate electrode material on the response of OECTs. We studied OECTs made from the conducting polymer poly(3,4-ethylenedioxythiophene) doped with poly(styrene sulfonate), and which utilized halide electrolytes. We demonstrate that OECTs with Ag gate electrodes show larger current modulation compared to OECTs with Pt gate electrodes. This effect is due to a change in the OECT regime of operation from capacitive, in case of a Pt gate electrode, to Faradaic, in the case of an Ag electrode.