This study reports evidences of dispersive transport in planar PbS colloidal quantum dots heterojunction-based devices as well as the effect of incorporating a MoO3 hole selective layer on the charge extraction behavior. Steady state and transient characterization techniques are employed to determine the complex recombination processes involved in such devices. The addition of a selective contact drastically improves the device efficiency up to 3.15 % (especially through the photocurrent and series resistance) and extends the overall charge lifetime by suppressing the main first-order recombination pathway observed in device without MoO3. The lifetime and mobility calculated for our sulphur-rich PbS-based devices are similar to previously reported values in lead-rich quantum dots-based solar cells. Nevertheless, strong Shockley-Read-Hall mechanisms appears to keep restricting charge transport, the equilibrium voltage taking more than 1 ms to be established.