Dense suspensions of soft colloidal particles display a broad range of physical and rheological properties which are still far from being fully understood. To elucidate the role of deformability on colloidal flow, we employ computer simulations to measure the apparent viscosity of a system of droplets of variable surface tension subjected to a pressure-driven flow. We confirm that our suspension generically undergoes discontinuous shear thinning, and determine the dependence of the onset of the discontinuity on surface tension. We find that the effective viscosity of the suspension is mainly determined by a capillary number. We present active microrheology simulations, where a single droplet is dragged through the suspension. These also show a dynamical phase transition, analogous to the one associated with discontinuous shear thinning in our interpretation. Such a transition is signalled by a discontinuity in the droplet velocity versus applied force.