Lithium ion battery impact of cycles on discharge rate
Unless you are short circuiting the battery discharge rate is dictated by the load connected rather than the battery cells themselves.

When a cells capacity has reduced the full and empty voltages remain the same, what changes is the maximum amount of charge stored within the cells. They will take less charge to reach the maximum charging voltage and so have less charge in them to discharge.

Also keep in mind that for Li-ions voltage is significantly impacted by temperature.