crown jewel vs precious stone

crown jewel and precious stone both are nouns.

Word	Noun	Adjective	Verb	Adverb
crown jewel	Yes	No	No	No
precious stone	Yes	No	No	No

As nouns, precious stone is a hypernym of crown jewel; that is, precious stone is a word with a broader meaning than crown jewel:

crown jewel: a precious stone that is a valuable part of a sovereign's regalia
precious stone: a precious or semiprecious stone incorporated into a piece of jewelry

Other hypernyms of crown jewel include gem, jewel.

crown jewel (noun)	precious stone (noun)
a precious stone that is a valuable part of a sovereign's regalia	a precious or semiprecious stone incorporated into a piece of jewelry
the most desirable assets of a corporation