This is a simulation of objects sliding and rolling down an incline. This is a simulation of four objects on an inclined plane. You can adjust the friction from the slider. The different mass distributions cause the rolling objects to have different rotational inertia, so they roll down the incline with different accelerations.
A certain portion of the energy each object starts with is converted into rotational motion, and the rest is converted into forward motion toward the finish line. The pre-factor in the moment of inertia then determines the balance between rotational motion and linear motion. For the roll of a ring, more of the initial energy is converted into rotation than into motion down the track, allowing the sphere to come out ahead. So what should happen if you match up the ring against a disc?