Both dramas feature a similar scenario where ML suddenly has to take care of two wives and two sets of children - ones from his "current" identity and ones from his "previous" identity. The difference lies in how the situation came about - Miracle That We Met he reincarnated and in New Face he had his identity changed (against his will).
The main idea of both dramas is that the main character literally swaps faces with someone else. In LRRFTF, the main character's family tried to kill her, and she swaps faces with someone to get revenge and find out the truth about what happened. In NF, the main character didn't choose to get a new face, someone forced him to. He is also trying to discover the truth about the past event. In both dramas, the protagonists search for the truth and investigate while pretending to be the person whose face they have.
In fact, apart from that, these dramas are very different, but they do have some points in common.
In fact, apart from that, these dramas are very different, but they do have some points in common.