Or maybe any compliments they WON'T give?
Alicia's go to metaphors or imagery when she describes Mrs. Moon is always things related to being divine and goddess-like. She associates her with being glamorous, pristine and immaculate, and so these are the sorts of words she usually uses when talking about or describing Mrs. Moon.
Melissa is usually associated with the image of a child in Alicia's head. She is very small and hyperactive, so she usually reminds Alicia of a giddy kid. Melissa personally associates herself with being childish because she still feels like she's 19, though people tell her she's too old to be so loud and hyperactive.
Alicia usually associates Kattar with a cat and a prince. Occasionally this cat is a lion, and occasionally being prince-like isn't actually a compliment, but those two images still stand in her mind. She associates him with being regal, a little secretive and also very chic, and like his mother, pristine.
Kattar associates his mother with divinity the same way that Alicia does, but it's a very different kind of goddess that he sees in his mind. He associates her with infallibility, analysis, and rigidness. She seems to be very liberal with him but really, it's a bit more like having a shock collar tied to an invisible 'fence' you run into and are shocked by when you don't see it coming.
He regularly describes Alicia in his own head as tiny, for one thing, but he also associates her with a flame. She's small, but she can leap up violently randomly. When she's in control of herself, that fire is warm, comforting and pleasant to be around, when she isn't, it really hurts. Also she's hot cough cough.
As for compliments, for most of their relationship up until this point Kattar has refrained from giving Alicia ANY compliments that have to do with her appearance which has really hurt her feelings, but she realized in the chapter "Playing Dress Up" that she's never given him a compliment like this either.
Now they are being more open about giving each other compliments. Kattar usually just says 'pretty' but in the chapter "Pacifier" Alicia kind of had a crisis about that.
On her part, she's called Kattar 'hot,' albeit by accident, but they are both pretty wary of using the word sexy lol.
For the most part, neither one of them compliment each other very directly very often. They're more in the habit of making statements that just show what they're thinking. Kattar thinks she's very talented, so he'll make statements like "I'll have to try that next time you take the world by storm" or "We can't be giving away signed artworks for free. They'll be worth a lot when you're big and famous."
On Alicia's part, she was really even less free with compliments than he has been, but she's working on it.