Coils are more "plush", more linear... Meaning that the amount of force required to compress the coil spring is relatively constant throughout the entire stroke. Many people feel that coil sprung forks are plusher, smoother, than air forks. Coil springs preload is either adjustable by turning some sort of screw and adding preload, or swapping for a stiffer or softer spring.
Air Springs are said to be more progressive, that is that the deeper into the travel you get the more force it takes to compress it further. Sometimes this can mean that for the first half of travel the fork feels pretty smooth, but it takes more force to compress it further in the travel so the bottom end can be more harsh. Air springs also need to be air-tight, and so have additional seals. More seals= more friction. Air springs are significantly lighter than coil springs. Air springs are preload adjustable based on the amount of air you put in and can be dialed in to a tighter tolerance than a coil spring.
If you are leaning toward an adjustable travel fork (I would caution you against, FWIW) not all manufacturers offer travel adjust in coil and air sprung versions. Fox for example, only has air-sprung TA forks....
Generally... if you don't mind a little extra weight and you fit into an "average" cyclist's weight class (say... 150-225lbs) then a coil is probably better (IMHO).
If you're a weight weenie just go get an air fork and never complain about how the fork works ever again.