The transfer of force by the application of liquids is known as hydraulics, while the same done using gases is known as pneumatics.
There are some advantages of using liquids rather than using gases. In vehicular brakes these advantages make it easier to use liquids in the braking system and they are given a higher preference than air.
The advantages of using liquids include the fact that liquids are almost incompressible and this prevents any absorption of the energy that has to be transferred. The fact that liquids are not compressed also increases the force that can be transferred. When gases are used as a medium to transfer forces, they retain the pressure that has been applied and this results in the piston that is used to apply the force springing back when the pressure is released. To solve this problem special bleed off valves are required. The use of liquids does not lead to this problem as a small movement of the load releases the pressure that is stored.
Using air instead of a liquid in brakes would make their use quite difficult as the initial force to be applied would be higher. When the pressure would be released from the brake pad it would spring back suddenly and there would also be a necessity to use a separate bleed-off valve to eliminate the pressure that is stored in the compressed air once braking is not required.