There's more similarities between these two besides the very similar poster (lol)...
Both mystery romances, with a chaebol/luxurious life backdrop. The male lead in KMHM must hide his multiple identity disorder from the rich, while the female lead in Mask must hide her true identy as a poor woman from the rich.
Similiar melodrama vibes

YOU! WHAT ARE YOU DOING NOT WATCHING THESE TWO!?! You're missing something great...

Both psychology themed and will make you think. Both deal with human darkness and tragedy: Love Shuffle in a way that will make you laugh and think; Memories of Matsuko in a way that will make you cry and think.
Both MUST WATCH. WATCH THEM NOW!

Psychology, depth, introspections featured in both. Same experimental and psychedelic athmosphere. Comedy with bitter darkness and biting black humor.

Fukatsu Eri No Black Comedy (short series, 20 eps x 3-10 min) will make you LAUGH about the absurdity of life, while Memories Of Matsuko (film, 2h 10 min) will leave you CRYING for over half of the film!

Both are essentially comedies but with underlying darkness, bitterness and depth. Psychology genre with introspections over humanity, life and love.
Recommended for fans of depth, psychology and/or dark humor lovers or just people with an overral cynical outlook on life and humanity.

Love Shuffle is 10 eps x 45 min,
while Fukatsu Eri No Black Comedy is 20 eps x 3-10 min

-Both include the love story between a Grim Reaper and a mortal human
-Both have a group of grim reapers doing their duty, in so, deal with life & death questions
-In both the Grim Reaper character is cute, unique and very lovable

In Universe's star the Grim Reaper/Human lovestory is the main focus/main OTP, in Goblin it's only a secondary leads/second OTP story.

-Both are tear-filled ROMANCE MELODRAMAS where the leads know each other for years and struggle to get maybe together
-Both have EXCELLENT main pairing with great CHEMISTRY

-Both are tear-inducing ROMANCE MELODRAMAS where the leads know each other for years and struggle through obstacles to get maybe together
-Both have AMAZING chemistry between the leads

-Both is about a love story between a korean man and a japanese woman, and the subsequent cultural clash between korean and japanese culture

-Both have an attractive korean male lead: T.O.P. in TSM and Won Bin in F2002
-Both are short: TSM is 18 eps x 15 min and F2002 is 4 eps x 50 min

DIFFERENCES:
-TSM is more artful/deeper meaning and has the better stunning cinematogtaphy and a more darker and mystical tone
-F2002 focuses more on the cultural difference, while TSM more on past hurts and love itself
-TSM is better than F2002

ALSO, Check out:
-Ueno Juri's AMAZING acting in TSM!
-Yoo In Na (Goblin, Queen In Hyun's Man) as side character in TSM
-Lee Dong Gun supporting role in F2002

-Both REVENGE ROMANCE MELODRAMAS, where male lead takes revenge on family (direct family & family-in-law respectively)

- Both have a leading male actor whose acting is AMAZING! (Green Rose: Go Soo. ISILY: So Ji Sub)

-I'm Sorry I Love You is better (10/10!) , so it's better to watch Green Rose first, other way around may feel like a step-down, especially GR male lead's trauma might seem very light in comparison to the trauma of ISILY male lead's.

-ISILY has a more sympathetic/tragic male lead than GR
-ISILY is more romance-focused & the love story MUCH better
-GR is slow-paced, while ISILY has a much better pace/doesn't drag or bore you

Both deal with Life/Death.

My Fantastic Funeral is about a dying-of-a-disease girl planning her own funeral who falls in love

Loss:Time:Life is weirder, with people having additional time after their deaths to make up for what they'd missed before they really die. No love story in LTL.

Both tackle deep Life/Death questions.

This is the korean remake version of the original Loss:Time:Life japanese drama.