The definition of torque is force times lever arm. As you state it, force and lever arm are identical, so is the torque.
There are differences. Because the moment of inertia differs, the applied torque will cause a different angular velocity (if the force is not in line with the centre of mass).
You are on the right track with your line of thinking, but as per our comments above, it may be better to think about applying forces to each ball as opposed to velocities. If you apply a force to each ball you can find the center of mass motion by summing all of the forces on all of the balls and using $\vec{F}_{net}=m_{tot}\vec{a}_{CM}$, where $F_{net}$ is the vector sum of all of the forces, $m_{tot}$ is the total mass and $a_{CM}$ is the acceleration of the center of mass.
To find the rotation of the body, you need to find the net torque about your axis of rotation. If there is no fixed axis of rotation that you set, the axis of rotation will be about the center of mass. For each ball, you can calculate the torque from the force applied from the equation $\vec{\tau} = \vec{r}\times\vec{F}$, where $\vec{r}$ is the vector from the center of mass to the ball in question (or from a different fixed axis of rotation), and $\vec{F}$ is the force applied to that ball. Note that the torque is also a vector, and points along the axis of rotation. To find the net torque, you can do a vector sum of all of the individual torques.
Once you find the net torque, you can then find the net angular acceleration $\alpha$ of the rigid body, by using the formula $\tau = I\alpha$, where $I$ is the momentum of inertia of your rigid body, which can be calculated using $I = \Sigma m_i r_i^2$, where this is a sum of the mass of each ball times the square of the distance from the axis of rotation (center of mass most likely).
The angular velocity of each ball is then given by the angular acceleration times the amount of time that the forces are applied to your object, $\omega = \alpha t$
Best Answer
Yes, it will affect angular velocity since different mass distribution have different moment of inertia $I$ in general. The effect of torque $\tau$ on the angular velocity $\omega$ of the object is given by $$\tau=\frac{d}{dt}(I\omega)$$
The moment of inertia of a point mass is given by $I=mr^2$, so in your case, the radius differ by 10 time so moment of inertia differ by 100 times and so does the angular velocity. Note that when you mention torque, you dont necessary need to specify which point it acts on.