Equal torques act on the discs A and  B of different moments of inertia I_A and I_B respectively (I_B>I_A), initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are  v_A and v_B respectively. We have

We know, relation between torque and angular acceleration is 

$\tau =I\alpha$

Therefore, for same torque applied

$\alpha \propto \frac{1}{I}$

Since $I_B>I_A$

${\alpha }_A>{\alpha }_B$

Since angular acceleration of A is higher than that of B, at any point of time linear velocity of a point on the rim of disc A will be higher than that of a point on the rim of disc B.