Basically it depends on the situation, like Maryam said. However, you may use it in any situation with the right word structure. For example" "I am angry at you." or "I am angry with you." Now, the phrase, "angry with you." could mean you are also angry for the same reason. Like, "I am angry with you." meaning "along with you." It is not a common phrase, however, you may use it.

I think they are similar and it's also depend on the conversation... For example. I know you took my car yesterday without my knowledge and I was going to be very angry at you. But mom explain to me why took the car without telling me. I wasn't going to call you back because I was angry with you.