Spring = linear ratio (ignoring progressive springs)
Air = progressive ratio
Now we got the physics out of the way here are the pros and cons in breif.
Coil
Pro - supreme small bump performance and grip, longer service intervals, no stiction.
Con - linear by design, if the frames kinematics (suspension design) is not progressive enough (rising rate) then bottom outs can occur on harsh landings and drops with a frame design that doesn’t have enough progression Or too low spring rate.
Air is infinitely adjustable in spring rate, coil shock takes spring rates in 25/50lb increments. It can be costly to get the goldilocks sag point. 25 or 30 is just a guide and some bikes work best well outside this ballpark. It could take several spring rates to find the right one meaning added expense.
Air
Pro - progressive by design for regressive or linear frame designs. Infinitely adjustable for spring rate and air volume within reason.
Con - lower performing small bump compliance when compared to coil (this gap has been bridged significantly recently)
Service intervals more frequent.
IMO, the ultimate is large volume air shocks with high and low speed compression and rebound adjustment, such as fox x2, cane creek double barrel air. Small bump compliance with added ramp up of air with all the adjustment in the world to suit any rider without custom tuning.
This is coming from a diehard coil fan too. I’ve seen the light.