pecking order vs power structure

pecking order and power structure both are nouns.

Word	Noun	Adjective	Verb	Adverb
pecking order	Yes	No	No	No
power structure	Yes	No	No	No

As nouns, pecking order and power structure are synonyms defined as:

pecking order and power structure: the organization of people at different ranks in an administrative body

Other synonyms of pecking order include hierarchy.

pecking order (noun)	power structure (noun)
the organization of people at different ranks in an administrative body	the organization of people at different ranks in an administrative body