Depends on which dual compound tires you're talking about. They have the Pilot Power 2CT and the Pilot Road 2, both of them have the dual compounds.
The Pilot Power 2CT is a bad expensive joke for street riders. The softer side only extends 1/2 inch from the edge, where street riders don't spend any time. The softer side also gets greasy and suirrelly with prolonged track riding. In other words, you are better of using the regular Pilot Power.
The Pilot Road 2, however, is an excellent choice for street riding. The center is harder than the standard Pilot Power, so it will last longer for street riding, and the softer side is the standard Pilot Power compound, and it makes up something like 60% of the overall tread area, not just half an inch. I personally am using the Bridgestone BT-021, which is a direct competitor for the Pilot Road 2. I have about 8,000 miles on it and it still has plenty of tread left. It also has plenty of grip for knee-down antics, if you are keen.