power structure vs pecking order

power structure and pecking order both are nouns.

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

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

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

Other synonyms of power structure include hierarchy.

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