We normally use all braking systems available to us. In fact, I know of one of our pilots who had one thrust reverser inop (a permissible unserviceability), one wheel brake inop (also a permissible unservicability), and automatic spoilers inop (permissible as long as they work manually) and refused to accept the aircraft in that state until one of the 3 "stopping" systems was fully serviceable. The flight with 250 passengers was delayed and the plane towed to the hangar while they found another one. Every other pilot I know would also have refused to accept it.
Where braking systems are applied automatically and are fully serviceable, we always use them in that mode. This concerns the ground spoilers and the wheel brakes.
Upon touchdown:
1) The ground spoilers extend automatically to dump lift when "on ground" (i.e., weight on wheels) logic gets applied.
2) Simultaneously the pilot activates reverse thrust (can only be done manually).
3) The wheel brakes operate automatically:
In a Boeing: there are 6 autobrake selections (1,2,3,4, Max, and RTO - rejected takeoff, which is equivalent to "this is going to be spectacularly violent" and only selected for takeoff). The autobrakes operate when the thrust levers are at idle and the wheels have spun up.
In an Airbus: there are 3 autobrake selections (low, medium, max - the "max" position is used on takeoff and will activate for a rejected takeoff much like the Boeing "RTO" setting). The autobrakes on an Airbus operate when the ground spoilers are commanded to extend, or in the case of the "max" selection which I've never seen used for landing, the nose gear is also required to be compressed.
The wheel brakes in both Boeings and Airbus operate to a "constant deceleration rate". So the application of reverse thrust, and the deselection of reverse thrust, affects how much brake pressure is applied to the wheels.
As a general rule, because the aircraft have carbon brakes and carbon brakes work better and last longer when they're applied harder, the Company prefers to use only idle reverse thrust where runway length and performance permits, and let the wheel brakes do all the work. However if there is any doubt, or particular taxiway exits need to be taken, we'll use full reverse thrust.