They are both dramas revolving a career-minded FL who finds peace in the quiet of rural Korea.
The stories are quite different, but both shows have the addition of a makjang revenge plot which is a bit detrimental. This is worse (in my opinion) in Eccentric! Chef Moon. My Husband Oh Jak Doo is a bit more consistent with its premise, but still there are some makjangish elements especially in the second half.

Okay, I admit it, these stories are nothing alike...BUT both have a second ML who's eccentric yet downright adorable!

In Shopping King Louis Cha Joong Won (portrayed by Yoon Sang Hyun) is a stylish, yet gruffy, city bachelor. In My Husband Oh Jak Doo, Eric Cho (portrayed by Jung Sang Hoon) is an insecure US-schooled parvenu who wants to earn prestige for his father's business.
Both actors play these roles with heart and humor and (even if both dramas also have pretty strong first MLs as well) they both often end up stealing the show.

These two second male leads fall in love with their respective dramas' FLs, but even if their feelings remain unrequited they support the women they love. They also begrudgingly form a sort of bromancy relationship with the MLs.
The only reason why I didn't suffer from SLS in neither of these shows is because I didn't want the FLs to steal these two...I mean...they are obviously both mine!

These show have a similar premise of a FL having to give up enrolling into university because of life circumstances, leaving the ML alone after highschool and meeting him up again many years later. The plots do get developed differently though.

In both dramas:
- in highschool the ML had a crush on the FL even if he never confessed;
- ML and FL lose contact after highschool and met much later on;
- ML has now a successful career;
- FL had a promising future when in highschool, but she couldn't pursue her dreams and is now in an unhappy situation;
- ML is quite childish and petty, but genuinely wants the FL to grow into her full potential

Differences:
- ML/FL relationship in highschool is a rivarly in Hello Again! and frienship in Twenty Again;
- in Hello Again! the FL has to give up university due to some family debts. In Twenty Again the FL needs to leave before graduation due to getting pregnant;
- the time jump from highschool to present day is of 10 years in Hello Again! and 20 years in Twenty Again;
- in Twenty Again, the FL is married and has a grown son. Her husband complains about her not being educated enough and wants a divorce, which propels her to enroll in the same university where the ML now teaches;
- in Twenty Again the ML is bitter towards the FL once they meet again due to his first love being completely crushed by her marrying another guy. In Hello Again! the ML is warmer and more supporting towards the FL right away;
- in Hello Again! we have more of an workplace setting, while in Twenty Again we see more of the university life.

They are both comedies where the ML is a conman. In both shows you really need to turn off your brain sometimes to accept the ridiculous situations, but they are entertaining and enjoyable to watch if you don't take them too seriously.
Also, both dramas have an amazing cast and work so well because of them. I particularly enjoyed both their villains.

Switch is about a conman realizing he's a doppelganger of a prosecutor and ending up taking his role to catch the bad guys. This drama has a break-neck pace and it's really entertaining. Sadly, while it does great with comedy, it has very weak emotional scenes. Switch has some minimal romance elements but nothing gets developed much.

My Fellow Citizens is about a conman unknowingly marrying a detective and somehow finding himself taking part in the elections to become an Assemblyman. This drama is less ridiculous than Switch, but I found it also a tiny bit more boring. It does work better in the emotional department though and provides some very moving scenes.

It's a VERY tentative suggestion, but both dramas rely quite a bit on dark humour which I've up till now found quite rarely in Korean dramas.
The plotlines though are completely different.

I Picked up a Star on the Road is about a young woman accidentally hitting a famous actor (while trying to take revenge on her boss) and thinking she has killed him. This makes her take his body home to find a way to dispose of it...but the actor is still alive and the 'attempted murder' turns into a kidnapping.
Sadly, IPSR turns into a more classic rom-com after episode 5, but till then it's a very funny and unconventional (for Korean standards) dark comedy.

Psychopath Diary is about a mid-30s man who's a timid pushover losing his memory and coming to believe he's actually a cold-blooded serial killer.
Psychopath Diary has no romance (barely some minimum elements), but the humour is more consistent than in IPSR and I generally found it a superior drama overall.

Both dramas have one main lead with shamanic abilities. Religion is also present in both of them even if in a negative vibe in Children of a Lesser God.
The protagonists in both shows have different sets of skills and team together (reluctantly at the beginning) to defeat evil.

Children of a Lesser God is somewhat lighter in tone (having some comedic moments here and there) and the antagonist isn't a demon, but a cult organization. It still does have some creepy and bloody elements and some pretty disturbing scenes of child abuse.
The Guest is more of a pure horror drama and has a bleaker tone in general. The antagonist here is a poweful evil spirit and not just evil human beings.

Overall I found The Guest to be the superior of the two, but Children of a Lesser God is an interesting drama as well and might deserve a watch!