In both dramas:
A group of righteous friends try to fight the "mafia" of the pugilist world.
Good vs Evil , Right against Wrong
Kindhearted people are trying to protect themselves and survive from the bloodthirsty greedy men.
Money seem to rule the world.
Epic fightscenes. Bad guys fight "with their brains" as well . They are smart, cunning and use several methods to take down the good guys (not just swords and fighting).
In this difficult situation love blooms into unexpected places.

In both dramas the couple is already married from the beginning of the drama and they used to love each other , but the male lead is a questionable character with many hidden secrets.
Both dramas are romance/thrillers with suspense
In both dramas it is implied that the male lead (husband) keeps the female lead (his wife) locked in the house (with the excuse of protecting her due to her health issues).
Those 2 dramas are very similar. In both dramas the male lead loves his wife deep inside, but he has a possessive attitude and is obsessed with control. Those are signs of abuse and therefore it's wrong to exist in a relationship.

Both dramas are : mystery/thriller/romance/investigation/palace politics/strangling for power/corrupted officials trying to overthrow the prince from his position/suspense/action.

In both dramas the prince is smart and kindhearted but he's constantly threatened by corrupted politicians whom want to kill him.
In both dramas the female lead tries to save the prince and together they uncover murders and secret organizations that try to overthrow the monarchy.
In both dramas the main leads fall in love slowly in the process and not instantly. The romance is mature , deep and meaningful.
Female lead in both dramas is a capable warrior, she knows how to fight, handles a sword better than most men , is smart and cunning and deeply in love with the prince.
Both dramas focus in the "fight between Good and Evil" .
Both dramas have this dark cinematography theme similar to thrillers, include deaths and tragic scenes were good people get sacrificed and killed for the power hungry royals. Haechi is more serious and tragic. Our blooming youth is more focused on the romance.

In both dramas the female lead comes back to life via reincarnation/time traveling and she wants revenge from those who killed her and her family in her previous life. Then she also meets again the male lead and for a 2nd time they fall in love with each other and also he helps her take her revenge. Both dramas are great and the main couples have great chemistry . For me , Lost track of time is superior to Jun Jiu Ling , because it has more character development, the romance is way more tragic and sweet and the plot is more complicated . Overall , both dramas are very similar.

Suspense , agony , phycological pressure , palace politics and battling to survive inside the palace and save your soulmate from death....
Those 2 dramas are identical. Action , suspense and romance all combined.
In both dramas the Emperor is a kindhearted young man who tries his best to be a good ruler but the corrupted officials try to bring him down /kill him.
In both dramas the emperor does everything in his power to save female lead whom he loves deeply.
Great cinematography in both dramas.
Every episode ends with a cliffhanger and leaves you wanting more.

Both dramas have master - apprentice forbidden relationship .
In both dramas the female lead is an orphan or she's abandoned due to a massacre and male lead saves her and makes her his apprentice

In Both Dramas:

---Male lead is a kind, highly intelligent and calculating prince who has learned to hide his true personality behind a carefree facade since the true "ruler" of the country is only corrupt officials
---Male lead tries to support the innocent younger 4th brother of the family and help him success the throne, instead of the evil 2nd brother.
---Male and Female lead join forces and try to uncover corrupted officials and expose the crimes of the 2nd (evil) brother. Second brother does anything in order to steal the throne, including numerous murders.
---Both dramas have a lot of action scenes combined with interesting palace politics ( I never got bored not even for a second) and romance.
---Both dramas have a good amount of Romance . Female leads are smart , kind and fight for justice and to protect their loved ones.
---The side characters have interesting back story and are all well written. This adds a lot to the "world building".
---Male lead despite being a Prince, he never cares about obtaining the throne. He only wants to protect the younger Prince from the evil older Prince whom desperately tries to win the throne.

Differences:
Well... Haechi is K-drama not Chinese and is dark but not as dark and sad as Rise of the phoenixes was. Rise of the phoenixes was very very tragic.
Haechi has a lot of sad moments but there are also many times that the main leads will manage to succeed! Rise of the phoenixes also was more focused on politics. Haechi has more action scenes and more romance (without to forget the politics aspect).

Both dramas are serious and focus on how important it is in life to be kind and fight for justice. Good against Evil. Love against all forces. Those are the morale of the story.

Both dramas are Romance/ Historical/ Political
In both dramas there is a prophecy that two sisters are destined to marry the emperor, and this prophecy forces them to get entangled in political affairs and live in the palace.

In both dramas :
- Female lead is a talented doctress , with strong personality but also feminine and cute.
- Male lead appears to be cold at first but he's just lonely
- Male lead has a position with political power and needs to handle militarily affairs
- Arranged marriage were the female lead is forced to get married
-Male lead has a misterious (supernatural) incurable disease which the female lead tries to cure
- Love /hate relationship turns quickly into passionate romance
-Merxat plays in "For married doctress" as the male lead and in " Legend of yun xi" as the second male lead

Overall those dramas are literally THE SAME lol
For married doctress is a little lighter though.