self-important vs arrogant

self-important and arrogant both are adjectives.

Word	Noun	Adjective	Verb	Adverb
self-important	No	Yes	No	No
arrogant	No	Yes	No	No

As adjectives, self-important and arrogant are synonyms defined as:

self-important and arrogant: having or showing feelings of unwarranted importance out of overbearing pride

Other synonyms of self-important include chesty.

self-important (adjective)	arrogant (adjective)
having or showing feelings of unwarranted importance out of overbearing pride	having or showing feelings of unwarranted importance out of overbearing pride