in one sense, hydraulics and air bags/air ride do the same thing... allow you to lower and raise your car as you please. but the technology is different:
hydraulics push fluid
air bags/air ride push air
both have their pros and cons, though most people today would say that air is the way to go (cheaper, don't have all the weight of all the batteries, and no risk of spilling fluid everywhere).
depending on the car, and presumed use of system, both hydraulic systems and air ride may need to have the chassis reinforced.
many suv's nowadays come with an air ride system (range rover, lexus gx, and lincoln navigator to name a few)... though it just changes the ridge height slightly.
*enter pic of impala on hydraulics*
*enter cars on air ride*
in short, if you want to get as low as possible, and raise it up when you want to, air ride or hydraulics are the way to go.