in competition withpreppreposition: Relates noun or pronoun to another element of sentence--for example, "a picture of John," "She walked from my house to yours."
(rival to)
与…相竞争 yǔ xiāng jìng zhēng
与…相较高下 yǔ xiāng jiào gāo xià
Coca Cola and Pepsi have always been in competition with each other.