Basically the same story but I think FH has more depth to the relationship between the ML and FL than MIFOL does.
Differences:
- FH FL is screenwriter and MIFOL FL is lyricist
- longer trip after fake marriage in FH
- I think ML in FH has more playful character than ML in MIFOL

Both male leads try to stop deaths while dealing with murderers and crime from their past. They both have superpowers from childhood that causes them to change how they live. Both female leads are strong characters who use the help of the male leads to solve crimes.