Disc brakes are now normal on many upper level road bikes; they've been standard on MTBs for some time now. They are better than rim brakes on many levels.
I think their most important advantage is their reliability over time -- in the hands of the average, non-mechanic, user. Like millions upon millions of cars, bicycle disc brakes need little attention and generally require nothing more than pad and sometimes disc replacement both of which are easy and quick to do. Because of their reliability -- in the hands of average non-mechanic users -- they shall win the day.
I saw this happen in the motorcycle industry and the auto industry. No one in either enterprise would now consider designing a vehicle with drum brakes. Drum brakes needed more maintenance and if ignored became quite dangerous. While the same can be said about disc brakes (if ignored they can become dangerous), however, drum brakes tend become less powerful over time and their users often do not notice their deterioration until they suddenly fail. Disc brakes, on the other hand, usually work the same until the pads wear out whence they proceed to scream and squeal scaring the crap out of the negligent owner sending him/her to the nearest brake shop.
Joe