The difference is meaning either permanent or temporary behavior.
"You are stubborn" indicates a general personality trait. It means that the person in question is always stubborn. Like "They are very polite" or "He is really condescending".
"You are being stubborn" just says the person is behaving in a stubborn way at that moment in time and doesn't mean they are always stubborn.
A: "I still think we should go with the other option"
B: "Now you're just being stubborn"
This works in the past tense as well. "You were just being stubborn" means the person was acting stubbornly at a specific moment in time. The exact moment is usually inferred from the context:
"Did you really like her presentation or were you just being polite?"
The first one is not as common in the past tense. "You were stubborn" wouldn't make much sense in most cases, as personality traits are not easily 'unlearned'.