There is alot of information available on various systems for paddle shifting with the 3 major types being Hydraulic, Pneumatic and Electric. Although each has its pros and cons, we have simplified the main parameters in a table summary for you.
When dealing with the high end of motorsport, speed and efficiency is critical to saving every critical millisecond. That is why hydraulics are the preferred option of the top teams worldwide.
Hydraulics can smoothly push / pull / lift and move loads because the hydraulic oil is not compressible, whereas air can become jerky and spongy as the air pressure fluctuates with cylinder movement or load changes, as it is compressible. In general a much larger pneumatic cylinder is needed to obtain the same force that a hydraulic piston can produce. The same is said for an electic actuators. To have the same speed and force, the actuator becomes extremely heavy.
Since compressed oil transfers far more energy than compressed air, nothing packs as much pound for-pound punch as hydraulic. That means hydraulics cans be a smaller, lighter tool design and deliver more power than even the biggest pneumatic alternatives!