important person vs influential person

important person and influential person both are nouns.

Word	Noun	Adjective	Verb	Adverb
important person	Yes	No	No	No
influential person	Yes	No	No	No

As nouns, important person and influential person are synonyms defined as:

important person and influential person: a person whose actions and opinions strongly influence the course of events

Other synonyms of important person include personage.

important person (noun)	influential person (noun)
a person whose actions and opinions strongly influence the course of events	a person whose actions and opinions strongly influence the course of events