desirable vs worthy

desirable is not a noun while worthy is a noun.

Word	Noun	Adjective	Verb	Adverb
desirable	No	Yes	No	No
worthy	Yes	Yes	No	No

As adjectives, desirable and worthy are synonyms defined as:

Other synonyms of desirable include suitable.

desirable (noun)	worthy (noun)
	an important, honorable person (word is often used humorously)

desirable (adjective)	worthy (adjective)
worth having or seeking or achieving	having worth or merit or value; being honorable or admirable
worthy of being chosen especially as a spouse	worthy of being chosen especially as a spouse
	having qualities or abilities that merit recognition in some way