Are dual pivot brakes quantifiably better than single pivot calipers?
Yes, there is a real substantial difference in mechanical advantage. This can be measured and proven, because it's simply down to leverage and the laws of physics.
It means that you can brake harder without having to pull/push the lever harder. You just have to move it a little further (because of course you can't get something for nothing). This particularly helps when braking from the "hood" position, when it's difficult to apply a lot of force.
The limiting factor to braking for me on a light road bike on clean dry tarmac in a straight line is the amount of deceleration possible without going heels over head, rather than tyre adhesion. I can comfortably achieve this limit with a dual-pivot front brake. I can't with a single-pivot without hurting my hand. You might have stronger hands?
Dual-pivot is not so important for a rear brake, hence Campagnolo's sensible option of dual-pivot front and single-pivot rear.
SPs are lighter and can cope better with a buckled wheel, and don't lock-up a rear wheel too easily. DP also has the advantage of better centering, though.