Recommendations

Cold ML in white suffering from lifelong disease is always keeping an eye and coming to the rescue to the fiery badass FL who misunderstands him. He is also key in her martial art training and turns her into a weapon that can possibly turn against him. Lots of duels between ML and FL and sexual tension.

Similar in atmosphere story and chemistry.
About the relationship, both are incompatible entities that work together to save people and solve mysteries.
Wonderful teamwork.
Both are horror comedies.

Both dramas include supernatural elements and revolve around a private investigator and his assistant

In both stories, the girl and the CEO starts on a bad foot but eventually got to know each other. The CEOs in both stories try to push an upcoming star in the spotlight as someone tries to push her down. In respect, there's a jealous ex in the background scheming around.

-over bearing boss
-funny banter
-boss/employee
-rivalry between second leads
-hyper couple
While they are two completely different styles the banter between the main couples are really similar. Both main leads have strong personality

Both dramas are about a virus suddenly being released and turning humans into monsters and the alive humans trying to fight back. In Kingdom the virus turns them into Zombies, and in Search the virus turns them into monsters with great strength that can infect humans they attack or kill.

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.

Similar. Both have some time travel. Both got secret(that they time traveled) can’t share with others. Love, angst

Hello, God is the korean adaption of Algernon Ni Hanataba Wo. In both movies, a learning disabled man is given the opportunity to become smart via modern technology.

Both movies are the same story; a learning disabled man faces some prejudice from his co-workers and mother. He is then given the opportunity to become smarter through an operation.
Algernon Ni Hanataba O has more of a romantic focus, and the main character's transformation from dumb to smart is much more dramatic, while Algernon Ni Hanatabo Wo spends more time showing the main character's struggle while he is learning disabled.

Very similar themes about a son running away from home and returning years later transformed and ready to claim property. Both have childhood friends as FL they are reunited with, and both MLs are misunderstood in their intentions (and both kinda scruffy-looking when they get back).

If you like a rural farm setting paired with a hyper-possessive male obsessed with the FL, both of these will fit. Raeng Tawan has a revenge plot directed at the FL, while in Pin Anong it's directed at others.

Both involve the business and dangers of birds' nest harvesting, and extended time on remote islands. But Mungkorn Suer has directly warring families, is set in the past, and has a faster-moving romance with stronger chemistry. Sampatan Hua Jai shows more detail of the nest-harvesting process, while Suer is more about competitors in the market.

Because they both are Philippines BL drama series.
I have never recommend anything so i don't know what to put in here.

Both female leads end up an evil extra in the stories they fell into.
Both dramas make fun of common drama tropes and are hilarious to watch.
Plus Tiger and Rose had this one line that can help calm everyone who suffered from Second Male Lead Syndrome in Lost Romance:
"The male lead belongs to the female lead. The second male lead belongs to everyone (audience)."

While Xiao En did not write the novel she ended up in (and hence does not know how it will end), Xiaoqian in Tiger and Rose falls into a drama script she wrote herself, which means her take on how to change her fate would take a different turn than Lost Romance.

Without spoiling the ending -- watch until the end, you'll find parallels in how the male leads are set up too XD