Her Phoenix Majesty

- Matriarchy setting
- FL forces ML to marry
- ML comes from a patriarchal society
- FL is an infamous playgirl princess
- Role reversal themes
- Comedies
- Same actress playing the queen in both dramas

- Matriarchy setting
- FL forces ML to marry
- FL is a playful princess
- ML doesn't like her at first
- Role reversal themes
- Comedies

- Matriarchy setting
- FL is an infamous playgirl warrior princess
- Gender role reversal themes in both
- ML becomes FL's consort
- Forced marriage (one-sided)

Stories and tone are different

- Matriarchy setting
- FL is flirty and forward, chasing ML first
- ML doesn't like her
- Gender role reversal themes
- Comedies

Main story of HPM, 2nd arc of CL
- Matriarchy setting
- FL forces ML to marry
- FL is a flirty and forward princess
- ML doesn't like her at first
- ML tries to escape from FL
- Gender role reversal themes
- Comedies

- Matriarchy setting (kind of, since MMH is set in the present world, but FL's clan is matriarch led)
- FL forces ML to marry
- ML tries to escape from FL's home

Both are mini dramas with a matriarchal kingdom setting and a princess FL.
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Both have a matriarchal kingdom setting and a similar plot in which the FL takes in the ML from another land as her concubine.