Well, as far as I know ferrite make the magnetic field density stronger. The magnetic field density is given by the product of the permeability of the material in question and the magnetic field. Usually, the permeability of ferrite is much bigger than that of the air, thus for ferrite the magnetic field density is much stronger.
The power, which is of interest, is proportional to the current and the variation of flux. The flux is proportional to the magnetic field density (it is not proportional at all times, but you get the ideia). So, the stronger the field density, the power should increase. You might think that the bigger the ferrite, the more power. However, you can only get as much power as your power input. So it might be possible that changing the ferrite once more does not get you that much energy.