Enormity: outrageous or heinous character; largeness of size, immensity.
Enormousness: largeness of size or scope.
Note: Use enormousness when meaning “large” and enormity when wishing to emphasize the awfulness of something.
Enormity is frequently used to refer simply to the property of being great in size or extent, but many would prefer that enormousness (or a synonym such as immensity) be used for this general sense and that enormity be limited to situations that demand a negative moral judgment, as in Not until the war ended and journalists were able to enter Cambodia did the world really become aware of the enormity of Pol Pot's oppression.
Fifty-nine percent of the Usage Panel rejects the use of enormity as a synonym for immensity in the sentence At that point the engineers sat down to design an entirely new viaduct, apparently undaunted by the enormity of their task. This distinction between enormity and enormousness has not always existed historically, but nowadays many observe it. Writers who ignore the distinction, as in the enormity of the President's election victory or the enormity of her inheritance, may find that their words have cast unintended aspersions or evoked unexpected laughter.