I think the lighter one will descend at a higher RoD.
I think you're right!
In basic aero we learned that an airplane will have the same glide ratio at its best L/D Angle of Attack, regardless of weight (let's discount residual thrust at idle). That means that even though the airspeed is higher for a heavier airplane at that AOA, the glide profile will be the same, and rate of descent will be directly proportional to airspeed.
Let's assume the heavier airplane is at its best glide speed. That means the lighter airplane will be at a speed higher than its best glide speed, and therefore at a non-optimum AOA. The lighter airplane will therefore have a worse glide ratio, and will descent faster at that airspeed.