Any question answered...

Pretty sure it only depends on the total energy stored in the battery, not the chemistry you use to achieve this, i.e. a 3V 2Ah Lithium cell contains as much extra mass when charged as a 1.5V 4Ah NiCd cell.

If the cell is a sealed system then I agree the electron weight should be the only difference but if the battery relies on its atmosphere to operate there may be chemical differences between the full and empty states that correspond with captured ions.