As moles consist of living cells located in the deeper layers of the skin (dermis), the best method for permanent mole removal remains that of surgery as surgical removal ensures all the mole cells are removed.
All the above techniques often result in partial removal of moles hence the likelihood of mole recurrence after treatment is often higher compared to surgery.
In my experience and opinion, I would rank CO2 laser superior to electrocautery (which is the same as radio-frequency electrosurgery) followed lastly by cryotherapy.
Unlike CO2 lasers, pigment lasers may be used to lighten moles but do not remove them permanently.