Both expressions are grammatically correct and convey a similar meaning, but there is a subtle difference in their usage.
"I want to be friends with you" is a straightforward and common way to express your desire to establish a friendship with someone. It implies that you want to develop a friendship with the person, emphasizing the state of being friends.
"I want to make friends with you" also indicates a desire to become friends with the person. However, this expression places a bit more emphasis on the process of building the friendship. It suggests that you are actively willing to take steps or make efforts to create and foster the friendship.
In most cases, the choice between the two expressions comes down to personal preference. Both convey the same basic idea, so you can use either one depending on what feels more comfortable to you. If you want a slightly more proactive tone, you might lean towards "I want to make friends with you." On the other hand, if you prefer a straightforward and simple approach, "I want to be friends with you" works well.