The main advantage is the ability to dissipate heat. Secondary is the availability of many component options.
Drum brake systems have the friction material and surface area located inside the drum. The majority of the heat created is absorbed by the drum and radiated to the atmosphere. There is very little air flow inside the drum creating an effect similar to an oven. During heavy or prolonged braking, this can eventually lead to brake fade. This is a condition where the shoe surface begins to melt and friction loss is experienced.
Disc brakes have both the friction material and surface area exposed to air flow. This allows heat to radiate from the rotor surface while the passing air assists in the heat removal process. There are more choices available such as vented rotors, larger diameter rotors, calipers, and brake pad materials.
In Drag Racing, we are concerned with the one big stop. This allows us to make the kit as light as possible while offering superior braking. Stock disc brakes are heavy since the extra material is necessary to preform well under constant on and off braking. The reduction of mass is why Drag Race brakes should never be driven on the street.