Bride of the Century (2014)

Both have female twins that haven't met each other until they were adults, the poor twin lead the rich twin's life for different reasons.

But in Bride of the Century, there is a supernatural element; while Mask does not.

both dramas feature an old, historic and conservative family that has to face a lively (future) daughter in law.
While the FL has to adapt to her new family, the family is changing because of her.
Similar is also the drama sweet 18 (https://mydramalist.com/294-sweet-18)

The big similarity between these dramas is the deception of the main female playing a rich (heiress) girl when she is actually rather poor and working several jobs. Money is the main protagonist into making them take this step (although Lee Da Hae plays more of a con artist, while Yang Jin Sung plays the hardworking innocent girl), which in both cases concludes into the girls falling in love with someone they supposedly have no right to. There is also a fall in the shower/barthroom scene in both dramas ;) Also, the forbidden love between siblings (as much as the leads can be considered siblings, when everything is only a con) takes on only a subplot in Bride of the Century, while My Girl lives out every angsty moment of it. Though, the big dissimilarity between these dramas is the supernatural/horror plot to the Bride of the Century - nevertheless, both dramas never fail to deliver the comical moments, as the girls bring their own breezy thinking into the lives of the stiffly rich.

Both girls can be lovingly called monsters ;)

They both have the evil moms, they both have a rich guy who falls in love with the main girl and they both have a main female lead who is hard working and kind.

both of male leadears are grumpy rich boys who fall for the poor girl and change after that

The story is the same. The difference is that there is no plastic surgery and betrayal on the part of the protagonist.

TVAS is more of a Suspense Thriller and BOTC is more of a Melodrama but what they have in common is a complicated Family connection, nefarious motives, and mystery to unravel. Also, a ghost.

both dramas perspective are towards marriage. even the genres quite different. we can see real chemistry between the leads. great cable dramas that we can't found on major broadcast network.

Identical looking actresses both into Male lead
Switch identities.

So similar, but with different personalities, what could happen when the two meet? A very cute and beautiful romance.

These drama have supernatural element and curse that bring the male lead and female lead together .

Both: are comedy mixed with melodrama (although I think BotC is a bit more dark and KMHM is a bit more cornball), have people doing dirty deals to try to inherit money/power/family business, feature a sibling-like relationship between the leading lady and the 2nd lead male, have a mystery surrounding both the leading lady and the leading man, leading men have trust issues due to people always wanting to take advantage of them for money, are well done.

Both female leads have doppelgängers where the poor female lead swaps identity with rich female character and breaks down cold domineering male lead with their positive and outgoing personality.

1) Marriage is initially unwanted/ arranged

2) Both mains are quite innocent and happy

3) Theme of duty and family honor

4)Though not as dramatic as TLE still exaggerated

5) Both mains marry into a complicated family

And finally...
Really enjoyed watching both dramas and was on the edge of my seat for most of BofTC's episodes.