Raimi

Both shows center on protagonists with tarnished public images—one a disgraced politician, the other a fallen TV reporter—who reinvent themselves by assuming family roles for political gain. In doing so, they develop genuine bonds with their new families, leading to personal growth and a deeper understanding of their values.

Both revolve around adults who attempt to use kids for their own interests and then end up growing attached to them.

Both father-son relationship genre.
Both are warm and heartbreaking.
If you've liked one of them, you will probably like the other

Both tells a story about a child who share similar circumstances.
The little prince is influenced by the french story with the same name.
Polaroid has a back story related to ice hockey.

Both have a main character who goes into an alternate universe where they are married and have children.
Welcome to life is about law while switch is about actors.

I found both stories pretty similar so if you liked one of them then you will surely like the other.
Differences:
Body/World swapped
Switch male lead is actor
Wonderful nightmare attorney

All of them talks mainly about the relationship between a stranger and twins. However, stepfather step contains action while marumo no okite is more realistic “except the dog part”.

Part of two stories are too similar, the only thing that makes good life better is the plot. It is really focused on the father-son relationship.