rivalry

There is a bitter/friendly rivalry between the two groups.这两个组织之间存在着激烈的/友好的竞争关系。

a strong sense of rivalry强烈的竞争意识

In our family there was plenty of sibling rivalry. [=competition or jealousy between sisters and brothers]在我们家，兄弟姐妹之间经常相互较劲儿。