criticism vs piece of writing

criticism and piece of writing both are nouns.

Word	Noun	Adjective	Verb	Adverb
criticism	Yes	No	No	No
piece of writing	Yes	No	No	No

As nouns, piece of writing is a hypernym of criticism; that is, piece of writing is a word with a broader meaning than criticism:

criticism: a written evaluation of a work of literature
piece of writing: the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)

Other hypernyms of criticism include writing, written material.

criticism (noun)	piece of writing (noun)
a serious examination and judgment of something	the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)
disapproval expressed by pointing out faults or shortcomings
a written evaluation of a work of literature