I disagree (which we always do about Silva LOL). For me, Drax’s actions are more a matter of the “motiveless malignity” Coleridge ascribes to Iago–all served up with a soupcon of fabulousness.
Maybe it is because I am a Buddhist, but it is because such feelings can be surmounted that Silva’s situation/response does not strike me as tragic (for that to be true there would have to be grandeur of some sort present). Same situation with SPECTRE: Blofeld was neglected and hurt, and his response is all out of proportion to what occurred (he just gets better mise en scene that Silva did). Blofeld would have been much more interesting as a character if, like Drax, he were depicted as “A being next to Devil—only not quite Devil.”
Sticking with Coleridge for a moment: “It is a matter of infinite difficulty, but fortunately of comparative indifference, to determine what a man’s motive may have been for this or that particular action. Rather seek to learn what his objects in general are!—What does he habitually wish? habitually pursue?”
As you say: Silva wants an apology. Drax wants to repopulate the earth with humans who will regard him as their new deity. I do not know whether there are more Drax’s or Silva’s in the world today, but those who have dominion as their object are for me far more dangerous than those who want an apology. As I see it, it is easier (and more likely) to maintain malignant momentum when it is grounded in a desire for dominance and control. If it is based on hurt–even a hurt felt at the core of one’s being–it is going to run out of steam–emotions are more evanescent than desires.