Similarities:
> both sageuk OTPs have great chemistry (lots of OTP moments towards near the end of the drama).
> both couples made so much effort to show how much they love each other and each of them proves how much they love their other half (especially true of the main male lead in Moon Lovers and main female lead in Princess's Man).
> side couples with their own stories (whether happy or sad) that made you care about them.
> lots of tragic events happening which makes or breaks the lead couples
> expect some tragic things happening among family members due to greed by some
> important theme in both dramas: filial piety vs love vs power
Difference:
> Most of the male lead characters in Moon Lovers (the princes) except for Wang So are played by actors in their twenties (when they made the drama), while the male actors in The Princess's Man (the 3 friends whose lives are changed due to events) are played by actors in their thirties (when they made the drama).
> You see a lot of politicking scenes in The Princess's Man while there's not a lot of those in Moon Lovers, more of the political dealings (example: King's dealings with various factions) are merely explained.
> Moon lovers is set in the dawn of Goryeo era while The Princess's Man is set in Joseon.

By the way: The Princess Man > Moon Lovers Scarlet Heart Ryeo for me

=> same male lead as played by Lee Joon Gi
=> Lee Joon Gi's characters are both suspected criminals
=> both dramas have adorable little girls, daughters of the male lead
=> the female love interests (mothers of male lead's daughters) don't know the criminal record of the male leads when they were dating
==> Trivia: both actresses for the love interests (Moon Chae Won in Flower od Evil and Park Ha Sun in Two Weeks) played as second leads in Han Hyo Joo's (Lee Joon Gi's love interest in Iljimae) dramas (Moon Chae Won in Brilliant Legacy/Shining Inheritance and Park Ha Sun in Dong Yi).
=> thriller drama with many plot twists and turns, most episodes keeps audience at edge of their seats
=> backstory romance of male lead and female love interests shown in pasts scenes throughout the drama
=> main difference: female lead in Flower of Evil is the detective investigating the male lead's case; while in Two Weeks, the female love interest has a detective fiance who investigates male lead's case along with a female prosecutor
==> female lead in Flower of Evil for me is like the composite character you get if you combined the female love interest, fiance detective, and female prosecutor from Two Weeks into one character.

Both are historicals where w woman pretends to be a man. There are many historicals where a woman pretends to be a man, but what makes this two shows similar is that the woman started to pretend to be a man after her brother's death (and she takes identity of her brother).

Shows are not similar except that Moon Geun Young is the lead in both shows.

However, I am doing this recommendation since I want more people to watch Painter of the Wind as it is a very underrated drama yet an extremely good drama. To understand how good this drama is, first of all the director is Jang Tae Yoo (who also directed another great drama in Tree with Deep Roots plus My Love from the Star and Lovers of the Red Sky). The direction he did in this drama is really good. Second, lead actress Moon Geun Young (who I noticed Catch the Ghost fans sometimes find annoying) won a Daesang in Painter of the Wind. Watch Painter of the Wind to understand how great her performance is as a woman pretending to be a man. Kim Yoo Jung is Moon Geun Young's child actress too, and her 2021 Lovers of the Red Sky show is a reunion of her and this drama's director (both shows have a female painter as a lead).
Drama is very unique, at first glimpse it might look like a simple age gap romance. But the truth is the female lead here has 3 love interests (an older man, a foster brother her age, and a female gisaeng/entertainer). Two of these relationships are two-sided and not one-sided.

I am recommending Painter of the Wind here because most people might know Moon Geun Young from Catch the Ghost (due to Kim Seon Ho recent popularity).

Not too similar except the fact that Lee Joon Gi is the lead in both dramas and the romance of his character and the female lead are crucial in both dramas.
However, I am recommending Flower of Evil to Moon Lovers fans because Flower of Evil is such an underrated drama and more people need to watch it. I know Lee Joon Gi has many fans from Moon Lovers, so I hope his Moon Lovers fans can watch Flower of Evil. Don't undersestimate the female lead, Moon Chae Won may not be the most popular to today's kdrama audiences but she is an acclaimed actress and she has great chemistry with Lee Joon Gi.
As for Flower of Evil fans, it is good to recommend Moon Lovers since it is indeed one of Lee Joon Gi's most popular roles, it's a good idea to watch it for Flower of Evil fans to understand why Moon Lovers fans hype Lee Joon Gi's role in this show so much. And Lee Joon Gi did a great job in this role too.

Both are historical dramas where the male lead is a monster of sorts, a female lead that sometimes dresses men's clothes, plus the female lead's father sort of paranoid sometimes. Drama plots are not exactly the same but the similarities above plus the way the female leads addresses the male lead as seonbinim (scholar) kinda made me remind the dramas of each other.

Both dramas are historical dramas with fantastical elements that stars Lee Joon Gi as the lead male actor. In Scholar, Lee Joon Gi is the more mystical character while in Arang, the love interest is the more mystical character. Actor Han Jung Soo appears as a “hunter of sorts” in both dramas.
Qualitywise, I find Arang and the Magistrate so much better, people should try Arang even if they find Scholar boring.

Both modern dramas of Lee Joon Gi. There are parts in both dramas where he lives in an identity different from his real one.
Actually the main reason I'm recommending Time Between Dog and Wolf is because I was most amazed by LJG in that drama. He's always amazing in almost all his dramas, but I'm most amazed with his acting in Time Between Dog and Wolf aside from Flower of Evil.

= Same lead actors as the main couple (I personally don’t find their chemistry the best in both dramas but the female lead is more bearable in Time Between Dog and Wolf than Gunman, perhaps because there’s a second more compelling female lead in Gunman).
= The actor who plays the real dad of the female lead in Time Between Dog and Wolf is the same actor who plays the dad of the male lead in Gunman in Joseon
= Father of a woman (female lead in Time Between Dog and Wolf, second lead in Gunman) who has a thing for the male lead is the one who killed one of his parents
= Male lead has two identities in both dramas, one before his supposed disappearances (death) and one after. His second identity is used to spy on the villain for the sake of revenge plus other things he or the organization he belongs to need to accomplish.

> Both are historical or at least have some historical parts
> Themes of reincarnation are present in both shows
> A murder mystery is central to the plot
> The supporting characters, especially the underlings of the lead guys, are very funny and are really great parts of both shows.

=> Shin Min Ah is so good in playing these cute mystical beings in an almost "impossible romance"
=> The chemistry between both leads are amazing
=> Male leads started out as somehow full of themselves but later grows as a character due to Shin Min Ah's character
=> One notable difference is there is no annoying rival female in Arang and the Magistrate, so you can watch Arang if you don't like those kind of characters.

> Same writers for both dramas (except Tree is based on a book by Lee Jung Myung)
> Two of the best historical dramas ever
> Smart protagonists and villains
> Debates and conversations on politics are interesting
> Great actors
> Shin Se Kyung is in both dramas