I'm intrigued... where is it exactly that the personality is displayed? Not in LotR or the Hobbit, definitely - as Morgoth was gone by then, and Sauron is far away and serves mostly as an incomprehensibly evil antagonist.
Is it in the Silmarillion? Morgoth spends most of the time there either being really, really angry, or sulking that he's not the lord of creation. Sauron's personality isn't elaborated too much upon in those stories either: he's the lord of tol-in-gaurhoth and does a lot of terrorizing and sneaking and torture, but do we get to see that much of his personality?
I haven't read the Children of Hurin, so it could be there. I haven't really looked into the History of Middle-Earth series either, there mgiht possible be there.