Answer
The raw egg will stop spinning in a shorter time.
Work Step by Step
Providing each egg with a torque $\tau$ gives each egg an angular acceleration of $$\alpha=\frac{\tau}{I}$$ since $\tau=I\alpha$. Therefore, as the moment of inertia increases, the lesser angular acceleration there will be and the less time it will spend rotating. Therefore, the hard boiled egg, which has a lower moment of inertia than the raw egg shell, will spin for longer. This means that the raw egg will spin for a shorter time.
