Why do some tectonic plates move faster than others? Is it due to friction between the plates, the driving forces on the plates, or both? If it is driving forces, what makes the driving forces on some plates stronger than on others?
The driving forces of plate tectonics has long been debated. Several mechanisms have been proposed, mainly ridge push, mantle drag, and slab pull (see this page from the British Geological Survey). However, there is now a good agreement that slab pull is the main driving force of plate tectonics. It means that it is the subducting plate which controls the velocity of the plate's movement. And the rate at which a plate sinks depends mostly on its age/temperature/density: older plates are cooler/denser, thus they sink at a higher velocity than younger plates.
As you suggested in your question, one of the things that slows plates down is friction with an adjacent plate. The force that drives them forward is the force of the mantle plume or plumes that split them off in the first place. A very large plume of magma rising from far below sometimes causes a plate to break off from a larger one, and a rift valley develops. Sea floor spreading from within the rift then causes the new plate to drift away, propelled by volcanic forces within the rift and by the mantle plume which still acts on it.
The consistency of the magma underlying the plate will also affect the speed with which it moves. The mantle itself is a plastic solid, but huge magma plumes rising from deep in the mantle lubricate the progress of the plate on top. These magma plumes vary in size and strength, therefore the propulsion they give to the plate they carry varies too.