offensive vs unsavoury

offensive is a noun but unsavoury is not a noun.

Word	Noun	Adjective	Verb	Adverb
offensive	Yes	Yes	No	No
unsavoury	No	Yes	No	No

As adjectives, offensive and unsavoury are synonyms defined as:

Other synonyms of offensive include unsavory.

offensive (noun)	unsavoury (noun)
the action of attacking an enemy

offensive (adjective)	unsavoury (adjective)
unpleasant or disgusting especially to the senses	morally offensive
causing anger or annoyance	not pleasing in odor or taste
for the purpose of attack rather than defense
morally offensive
violating or tending to violate or offend against
causing or able to cause nausea