Both dramas have a strong female lead and a dumb male lead.
Both dramas are funny but Choon Hyang has a more melodramatic moment compare to Fight for My Way. Both males lead have someone else as their first love and their close friends also become a couple.

Both are an interesting drama to watch. Choon Hyang is underrated here but it was considered a very successful drama during the first wave of K drama. I encourage you to try it out.

Both are asadora from NHK. The main character both came from Tokyo to the countryside. Both dramas also have the strong appeal of the culture and lifestyle of the countryside. Amachan was set up in Iwate, whereas Mare was set up in Noto. Both drama also offers a story of friendship and life journey. There are so many things that happened in life which does not always works in your favor, but the main characters are working towards their goals.

Personally, I prefer Mare compare to Amachan. I find the main character in Mare is more likable and mature. In addition, Mare story has more closure since it portrays her journey from childhood until adulthood and her character grown was shown very strongly compare to Aki.

However, Amachan also has some stronger strength. I find Amachan story is more realistic and not overdone with too much comedy (If you prefer realistic compared to fun watch, you might like Amachan more. In opposition, Mare has many weirds characters but also likable.), it also brings back memories of the old idol culture and nostalgia.

Both are about baking and pursuing a dream. This drama has a more heavy conflict with the main character being an illegitimate child of a Bread company CEO.

Both theme about food. Bread love and dream is more focus on relationship and drama than Tenno no Ryoriban. But both also has a strong theme about family.

Kimura Takuya played in both drama. Both drama has a 90s feel into it which bring the feeling of nostalgia.

Amami Yuki played in this drama too. Both are crime dramas with a tough female as the main character. I truly enjoyed both drama.

Both drama is about a person pursuing a dream, about food and family. Both dramas are heartwarming with lots of life messages. However, Tenno no Ryoriban is based on a real life person, whereas Mare is fictional. Mare also has longer episodes compare to Tenno no Ryoriban.