Electrorheological fluids offer potential for developing rapidly actuated hydraulic devices where shear forces or pressure-driven flow are present. In this study, the Bingham yield stress of electrorheological fluids with different particle volume fractions is investigated experimentally in wall-driven and pressure-driven flow modes using measurements in a parallel-plate rheometer and a microfluidic channel, respectively. A modified Krieger-Dougherty model can be used to describe the effects of the particle volume fraction on the yield stress and is in good agreement with the viscometric data. However, significant yield hardening in pressure-driven channel flow is observed and attributed to an increase and eventual saturation of the particle volume fraction in the channel. A phenomenological physical model linking the densification and consequent microstructure to the ratio of the particle aggregation time scale compared to the convective time scale is presented and used to predict the enhancement in yield stress in channel flow, enabling us to reconcile discrepancies in the literature between wall-driven and pressure-driven flows.