The ideal ground plane should be perfectly conducting and infinite
(according to John Kraus in his book Antennas). It is true that the
"measured impedance of a stub antenna varies appreciably as a function of
the ground-plane-diameter", but the variation diminishes as the diameter is
increased. Large square ground planes result in less variation than round
ones.

From the standpoint of radiation shielding, the larger plane should be
better than small ones.

Colin