Mechanically, the focus on the car is running more of the symmetric suspensions because you will have to turn left and right. You also want a car that changes direction very quickly. So the car is going to be a lot less stable than on an oval situation where you want the car to have an immediate reaction and some pitch sensitivity. One of the biggest problems on road courses is understeer, in which the car will tend to go straight when cornering. You want the car to react quickly, but also not go into oversteer during power applications.
Engineers make the cars more stable for oval tracks.
For superspeedways, teams go with a mechanical setup that provides the most grip as possible so as to reduce drag and improve speed down the straight. The cambers are all tipped into the corner negative cambers on the outside and positive cambers on the inside. The aerodynamics are biased to keep the balance in the middle of the corner, while allowing you to go down the straight as fast as possible. On an oval you don't want the car to be too quick turning into the corner, yet you don't want to have a lot of understeer. So there is a very fine balance between keeping the car stable, but also letting it carry a lot of speed through the corners.