ML is a supernatural doctor...
ML has been waiting for the FL for a long time after he lost her in the past.

Creative FL and cold producer who is actually a sweetie
Meddling and well intended ML mom who helps the couple getting together
Forced cohabitation
FL owes money to the guy
Both ML have a childhood trauma even though it is more the focus in Hello Mr Gu

Both stories have :
-ML seems cold and ruthless but is actually really sweet and kind
-FL has a "sleep" problem and the only cure is the ML by her side
-ML is involved in telling stories : in SP, he is the narrator of the story and invents stories for his wife, in PL, he is a producer of fantasy movies/animations

Same production
2 secondary characters are the same
Both cheesy and ridiculous but enjoyale
ML are somewhat a bit similar in their style and personality

Split personality.
Male confused about the mood swings of the FL
Elements of supernatural
A tad cheesy, not very serious

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.

-Palace intrigues with princes vying for crown prince position
-partnership between cunning ML and resourceful FL, with a love/hate relationship
-in Rise of Phoenixes, FL has to promise her mum never to marry ML, and in Legend of Hao Lan it's the ML who has to take a similar oath to his father, so your OTP is kind of doomed from the get go
-stellar cast of amazing actors, topnotch sets and costumes