Air Theory
An airbag naturally gives to provide suspension. The main key to a good ride in an air system would be to take the airbags' weight-handling capabilities into account and position them to get adequate pressure to make them act correctly. Add that with shocks and your ride should roll smoother than stock. In order to make an air system reliable, the most important and overlooked aspects would be keeping water out of the system, keeping the bags from rubbing anything, keeping air line isolated from heat, and running a heavy enough gauge of wire for your compressor.Airbag - The advantages of an airbag to a hydraulic cylinder is that it has a superior collapsed-to-lift ratio of up to four times as well as being able to act as a spring. The disadvantages are the diameter of the bag as well as the rubber's inability to handle constant rubbing, which would lead to a blowout.
Airbag - The advantages of an airbag to a hydraulic cylinder is that it has a superior collapsed-to-lift ratio of up to four times as well as being able to act as a spring. The disadvantages are the diameter of the bag as well as the rubber's inability to handle constant rubbing, which would lead to a blowout. | 
Compressors - A compressor would be equivalent to a hydraulic pump. The air tank (or tanks) is filled with one or multiple compressors to give you air on demand. Problem is that they take a while to fill your tank and are pretty hard on your battery and alternator when used with a multiple compressor setup. | 
Air line - Air line is nice because it's easily prepared with simple tools. Air line is usually plastic or some sort of poly, so it isn't that susceptible to exhaust heat. |
Air System as a Whole:
Pros: Air stains are easily removed, air gauge gives you an idea of ride height, easier to set up for a decent ride.
Cons: Air leaks are harder to find, air tanks are not space savers, regular air tanks are low pressure and have to be constantly refilled, if you have nitrogen you have to take the bottle to be filled, air is loud.
Hydraulic Theory
In hydraulics, the misconception is that they ride horribly. Hydraulics are made to handle such extreme conditions that they are rated for thousands more pounds than an automobile could deliver. They are used in every commercial application known to man. A new high-tech hydraulic suspension has even been used by the Spanish company Creuat for a racecar for the 24 hours of Lemans, the most enduring race in the world. The problem is that they don't give whatsoever. So in order for a hydraulic system to ride smoothly, the key will be to build a functional suspension around it. In order to achieve this, springs, accumulators, and shocks would be used. For dependability, we'll show you the latest and greatest that CCE has to offer.
Hydraulic System as a Whole:
Pros: Faster speed is as easy as adding more voltage (i.e., more batteries), made to handle extreme pressure, same ride quality at all heights.
Cons: Hydraulic fluid costs money, oil stains, have to replace seals, you need to store multiple pumps and batteries, no gauge of height, batteries are heavy, batteries have to be charged often.
Hydraulic line - Hydraulic line used in automotive applications runs up to 4,000 psi and has steel braided reinforcement; heat is not an obstacle. The thickness of the line is larger than air line and can be tough to run. It's more expensive and has to be prepared by a shop with the correct tools.Hydraulic cylinder - Hydraulic cylinders are made to handle extreme pressure and can withstand a beating. They are made of hardened steel and can rub on pretty much anything within reason. | 
Hydraulic Cylinder - Hydraulic cylinders are made to handle extreme pressure and can withstand a beating. They are made of hardened steel and can rub on pretty much anything within reason. | 
Dumps - There aren't as many standard dumps in the automotive market, but they are tried and true. If it isn't broke, don't fix it. High-end dumps can become very costly but aren't needed in standard applications. |
In the image here, the nitrogen gas is represented in red and the LHM fluid is represented in green. The fluid basically pushes the balloon and allows the fluid in the cylinder to give. This is the hydro-pneumatic equivalent to the spring being compressed and then rebounding. The pressure of the gas is the equivalent to the spring weight.