The huge difference, though, is that Katherine is explicitly coded as EVIL, she's a villain so everything she does is bad (including what she did to S&D), while Damon is one of our heroes, who clearly is supposed to have a redemption arc and who the show always codes as funny, sexy, misunderstood. And when Katherine kills/rapes people, the reaction is disgust and 'she must be destroyed', and when Damon does the same thing the reaction is 'oh no, poor Damon isn't doing well, he must be redeemed'.

And I mean, I don't love Katherine in the way you love Damon! I love her in all her unapologetic evilness, because I like a well-rounded female villain! :)
(I think we both have too many feelings? :P)