Think of what the normal force's "job" is to do in each case.
In the inclined plane the normal force just keeps the object from accelerating "into" the plane due to part of the mg force (the part perpendicular to the plane). Thus I argue that the Normal force must be a bit smaller than the mg force in this case. Since the acceleration is perpendicular to the normal force we notice that it is not a contributor to the acceleration.
In the banked curve, the normal force must not only keep the car from accelerating into the plane but now also must provide for the centripetal acceleration the car experiences. Clearly it must be larger than in the previous case. Since the acceleration is horizontal, it is the normal force that must be broken into components so as to provide 'some' force in that direction. The vertical gravitation force can not be responsible for a horizontal acceleration.
Last conceptual thought. Think of your foot being between the tire and road in each case. Would it hurt more if the tires rolled over your foot as in an inclined plane or in the banked curve. My bet is the banked curve would be much more painful. The foot experience a force similar to the Normal force.
Hope it provides some iinsight into this problem in a little different way than the traditional analytical method.