Jack Napier is a little full of himself. And by "a little" we mean that he is so full of himself that he's overflowing. There is no room for anyone else in his conceited egosphere. And if you think his vanity is bad now, wait until you get a load of Joker.
LT. ECKHARDT: Giant, menacing, supernatural form. Kind of like a bat.
Batman appears only at night, which makes people unsure of exactly what he looks like. And like with many things unknown, people begin exaggerate his appearance until he's something supernatural in form.
[JOKER goes from almost crying to laughing hysterically after seeing his own face.]
At first, it seems like Jack Napier is upset to be permanently disfigured by the acid bath. Then he seems to enjoy it. Does Joker think he looks better as, well, a joker? Or does he decide he just has to own it, and the rest of his "career" as a homicidal criminal is him making the best of his new face?
JOKER: Wait till they get a load of me.
Just as Jack was proud of his appearance, Joker is equally vain, if not more so. This guy would think he looked good if he swapped faces with a donkey's rear end. He tells people he looks good, and people think he looks good.
JOKER: You're beautiful in an old-fashioned kind of way. But I'm sure we can make you more today.
Joker thinks his personal ideal of how women should look is something to impose on all women, whether they want it or not. He appreciates Vicki Vale's old Hollywood glamor, but he thinks she should be modernized. And he's so full of himself, he thinks she'll go along with the suggestions.
JOKER: You know how concerned people are about appearances. This is attractive, that is not.
Joker says this immediately after the last quote critiquing Vicki's appearance. This is the pot calling a whole wall of kettles black. Joker accuses others of being concerned about appearances when 99.9% of his attention is focused on his own appearance. The other .1% is directed toward the appearances of others.
JOKER: She's just a sketch, really. […] You see, Miss Vale, Alicia's been made over in line with my new philosophy. So now, like me... she is a living work of art. I'm no Picasso, but do you like it?
Joker's strategy for validating his own appearance as attractive is to make attractive women, like models, look like him. If models are pretty, and models look like Joker, then Joker must be pretty. It's like the world's most twisted SAT question.