You Do Need power plug adapter while traveling from Switzerland to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Switzerland are C and J. This is how they look like.

Switzerland

In Switzerland, outlets of type C and J are in use.

Type C

Type J

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L