区别就是两者意思是不一样具体的不同如下

compete with，竞争常见释义

英[kəmˈpiːt wɪð]

美[kəmˈpiːt wɪð]

例句

We ask for a level playing field when we compete with foreign companies.

我们寻求一个能与外国公司公平竞争的环境

compete against，网络

竞争;对抗;与……竞争;

例句

It made it almost impossible for the smaller retailer to compete against the multiples.

这使得小零售商几乎不可能跟连锁店竞争。