unkindly vs unsympathetic

unkindly and unsympathetic both are adjectives.

Word	Noun	Adjective	Verb	Adverb
unkindly	No	Yes	No	Yes
unsympathetic	No	Yes	No	No

As adjectives, unkindly and unsympathetic are synonyms defined as:

unkindly (adjective)	unsympathetic (adjective)
lacking in sympathy and kindness	not sympathetic or disposed toward
	(of characters in literature or drama) tending to evoke antipathetic feelings
	not agreeing with your tastes or expectations
	lacking in sympathy and kindness
	not having an open mind

unkindly (adverb)	unsympathetic (adverb)
in an unkind manner or with unkindness