In what ways is a dual pivot brake better than single-pivot? How exactly is a dual pivot brake better than single pivot?

Is it the travel, mechanical advantage, or what?
The main point of a dual pivot is the mechanical advantage. Since the individual pivot for each side of the brake is optimized for a greater lever length, you end up with a greater pressure of the pads against the rim.

Also, since the pivots are cleverly positioned (in my opinion), you end up with a compact, light and strong overall structure.

The downside would be tire clearance, which is not big problem on road bikes. On mountain bikes, V-brakes provide very good mechanical advantage with a very good clearance, but with a less compact structure.