In our family there was plenty of 'sibling rivalry'. [=competition or jealousy between sisters and brothers]
There is a bitter/friendly 'rivalry' between the two groups.
a strong sense of 'rivalry'
(..) Is there any particular reason why you're such a bitch to me? Yes. Because it's my mission in life to destroy you. Well, nothing like a bit of interoffice rivalry to get those competitive juices flowing. Hannah, a word. - What do you think you're doing? - I don't know. It came out. (..)1998 TvShow: Charmed Title: The Truth Is Out There... and It Hurts Season: 1 Episode 8