In reply to bpmclimb:
Yet another discussion on an old subject, but still some of the main points have not come out clearly.
The fact that the ATC *and* the Grigri have both been fantastically successful devices shows that both have their place and there is not a clear-cut winner. The same goes for double and single ropes.
The main advantage of the Grigri is it is a self-locking device. The main advantage of the ATC is that the rope moves through the device more or less symmetrically, allowing for continual and rapid paying out and taking in. And yes, the amount of dynamism can be controlled with the ATC (by the angle of the rope to the brake hand). Both kind of devices can fail catastrophically: the Grigri if the brake lever somehow gets jammed open, the ATC if the belay hand somehow becomes disengaged.
The reason that pairs of climbers doing speed ascents use a Grigri (for the second man) is so that the rope is locked off whilst the second man's hands are otherwise employed, i.e. climbing. Most climbers regard the ATC as generally the more suitable device for trad climbing, and the Grigri for sport climbing.
The main advantages of double ropes is that they reduce drag and allow the climber to rappel the full length of the rope. The main disadvantage is more rope management. Weight is not such a disadvantage, because a full-weight single and a lightweight double weigh about the same.
The main advantage of a single rope is simplicity, although this is simplicity at the cost of redundancy. The advantages of double ropes over singles have diminished with time, as the length of ropes has increased and their weight decreased. Climbs outside the UK tend to be more straight up and down than elsewhere, so that double ropes are seldom needed for the climbing itself. Not only have ropes become longer, increasing their rapelling range, the routes themselves have tended to become "better" equipped for rapelling with single ropes. However, if in doubt on multipitch or mountain routes, double ropes are still the sensible option. Having the ability to rapel down a route has its merits!
Also, the distinction between twin and double ropes has diminished as ropes have become thinner, so that in practice one *can* use doubles as twins, even if this is not strictly recommended.