The string attached to the hoop has a greater tension.
Work Step by Step
The hoop has more mass spread farther from the center, so the hoop has a higher moment of inertia than the disk. As each mass falls, the gravitational potential energy of the mass is converted into kinetic energy of the falling mass and rotational kinetic energy. Since the hoop has a higher moment of inertia, it will take a higher fraction of the total energy in the system. The mass attached to the hoop will fall more slowly. Therefore the tension pulling up on this mass must be greater than the tension pulling up on the mass attached to the disk. The string attached to the hoop has a greater tension.