each other vs us

each other

pron
  • To one another; one to the other; signifies that a verb applies to two or more entities both as subjects and as direct objects 

us

pron
  • Me and at least one other person; the objective case of we. 

  • Me. 

  • Our. 

  • Me (in all contexts). 

det
  • The speakers/writers, or the speaker/writer and at least one other person. 

How often have the words each other and us occurred in a corpus of books? (source: Google Ngram Viewer )