You Do Need power plug adapter while traveling from Anguilla 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 Anguilla are A and B. This is how they look like.

Anguilla

In Anguilla, outlets of type A and B are in use.

Type A

Type B

Vatican City

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

Type C

Type F

Type L