I find them similar mostly over how natural the romance and the relationships were acted out and presented.

First things first the characters arent exactly likeable. You might experience the same kind of irritation. Mind your blood pressure while watching.

Both drama have:
A director type ml that deals with trauma and psychological issues that are tied to his childhood, a doctor fl who helps him throughout, bickering, emotional scenes, company conspiracies and power struggles.

In both drama the mls decide to "infiltrate" in another house in order to achieve certain goals but they find themselves falling for their roommates.

Both drama have the same feeling to them, hardworking ml and a sheltered princess fl who come closer despite their differences.

Both drama have : A teacher/mentor figure who do their best to help out each of their students ans students who face various problems in their lives. Towards the ending there are also a couple more similarities which wont be mentioned for the sake of not spoiling the drama to people who wish to watch either of them.

In both drama the mc is an unconventional teacher that tries to help their students and make them better people. In both drama there are heavy topics that are addressed both through touching monologues and dialogues and through comedy.

Basically the mcs are teachers that are trying to teach some morals and new mindsets to their students so as to help them not become pieces of trash later on. One of course tries to teach them in more extreme ways than the other. Both drama address heavy societal topics and deliver strong messages.

Both drama revolve around the topics
Music and rural life, love and finding your path in life. What makes you happy in life?
(Though Modern Farmer is more of a comedy while My Husband Oh Jak Doo is more of a melo)

Leaving the city to live in the countryside, finding oneself, food, hilarious moments, friendship and a dash of a love story.

Both drama are about a person who decided to leave the busy city life and reside in a small town and they try to find themselves again.

In both drama the mc is a consort in the palace who doesnt really want to be part of the intrigues. They would rather spend their time leisurely instead. That of course doesnt stop our ml from falling in love with them. Both drama are lighthearted and focus more on the comedy.