Have a look on how the earth's magnetic field is modeled presently:
he Earth's magnetic field is attributed to a dynamo effect of circulating electric current, but it is not constant in direction.
So the question becomes why the circulating currents have a higher effect on the northern hemisphere than the southern one. It evidently depends on how the magma in the center of the earth is oriented and the dynamo effect appears.
Convection drives the outer-core fluid and it circulates relative to the earth. This means the electrically conducting material moves relative to the earth's magnetic field. If it can obtain a charge by some interaction like friction between layers, an effective current loop could be produced. The magnetic field of a current loop could sustain the magnetic dipole type magnetic field of the earth. Large-scale computer models are approaching a realistic simulation of such a geodynamo.
So the details are not known, but the difference will be due to the geological topology of the earth.
For an intuitive understanding, take a bar of magnet. The north and south are joined rigidly. Turn the middle portion to a fluid, with a different density from north to south, you could then in a rotation have the north turning in much larger circles than the south.
In a sense , if the dynamo is fitted successfully we will learn something about the composition of the earth, solid-fluid.