The enhancement by ion-neutral collisions of the momentum delivered to ions for specified power is compared for acceleration under electric and magnetic pressures. The enhancement in both cases is shown to be proportional to the square-root of the number of collision mean-free-paths when neutral-gas density is low and to the number of collision mean-free-paths when the neutral-gas density is high. The distributions along the acceleration channel of the ion density and velocity and of the electric potential are calculated at the space-charge limit for acceleration by electric pressure and at the diamagnetic-current limit for acceleration by magnetic field pressure, for both collisionless and collisional ions. Optimal magnetic field profile is found for acceleration under magnetic field pressure. Accelerating ions colliding with neutrals under magnetic field pressure can provide a high thrust at a low accelerating voltage.