people tend to approach this issue from the wrong direction. imo. you often see people asking why coilovers are better than set dampers, and asking who is really going to bother adjusting them all the time.
i personally think that it is not so much that coilovers are better specifically, rather that better suspension is normally made as coilovers.
the internals are where the difference is, in the valving system. which ultimately controls ride quality.
for me the disadvantage is that you have to spend more money to have them set up properly, but the advantages (if you spend the money) are a much improved ride and greater stability.