The thing about SATA III not delivering its 6Gb/s, is regarding to its controllers.
Some Intel motherboards, for example, do not have native SATA III controllers. Intel uses controllers from another company -- Marvell Controller, for instance, which doesn´t performance as good as its native SATA II.
My motherboard has SATA II and SATA III ports, but I connect my SSD, which is SATA III to the motherboard native SATA II (with Intel controller), because Marvell Controller is crap!
EDIT: As for HDD is doesn´t matter if it is SATA II or SATA III -- it will not make any difference.