I have three different setups, each has it's place.
Electric die grinders:
pros; very portable , can be relatively low cost as only one item to purchase
cons; a bit bulky in the hand for fine work, because the motor is in your hands they are heavier than other choices, tend to get warm, internal cooling fan really stirs up the dust
Electric flex shaft grinders:
pros; portable, small handle(s) =better fit in hand, can run for hours and hours with little maintenance, can be run both clockwise and counter clockwise, variable speeds are nice
cons; good ones are higher priced initial investment,
air tools;
pros; light weight, can be had at low cost (for just the tool only), good amount of power and torque, no harm done if you stall the tool out ( no motor to burn up or shaft to break)
cons; exhaust air can stir up a lot of dust, cold in hands to operate in unheated garage during winter, oil in exhaust air can get on your project, added cost of compressor to provide the air required.
Good point about the airline getting saturated with oil if you also use it for painting. What I do is run a tee after my water separator and before my in line oiler. The air tools run off the line with oil and the paint guns run off the line with out oil. I don't interchange the hoses for either.
For my carving needs, I primarily use a flex shaft, specifically a Foredom.
There really is no one choice that will be best for everyone's situation. Heck, I've seen some guys using axes and gouges and knives. ;>) ;>)
