For me, the brilliance of the twin-pivot sidepull is the interconnection between the two lever arms. This interconnection obliges both arms to act in unison. Single-pivot sidepulls often suffer from one pad hitting the rim first, which then provides the resistance to pull the other pad on to the other side of the rim. On release, the brake blocks of single-pivot sidepulls are seldom equidistant from the rim.
Centrepulls are largely immune to this problem but at the expense of some extra weight including the hangers and straddle cable. Even so, centrepull designs using brazed-on fittings may well be a bit lighter overall than the alternatives.
Aesthetically, I find centrepulls make a bike look cluttered; especially the bigger-is-better versions such as the old Mafac Tiger. Twin-pivot sidepulls can be made neat and compact and, of course, have none of the hangers and additional cable stops of centrepulls.
I have no personal experience of disc brakes but I find Chris Boardman's comments sound sensible. Given the extra hassle for wheel changing, I would not be surprised to see discs gradually retreating to MTBs as time goes by. They must be more aerodynamic but an extra 30" taken in a wheel change can be the difference between getting back in the bunch and ending up in the autobus.