take sides with vs take someone's side

take sides with and take someone's side both are verbs.

Word	Noun	Adjective	Verb	Adverb
take sides with	No	No	Yes	No
take someone's side	No	No	Yes	No

As verbs, take sides with and take someone's side are synonyms defined as:

take sides with and take someone's side: support someone (as in an argument)

take sides with (verb)	take someone's side (verb)
support someone (as in an argument)	support someone (as in an argument)