Romeo and Juliet do respond differently to Romeo’s exile, but both go to Friar Lawrence and take his advice.
When Juliet finds out that her lover killed her cousin, she reacts with antithesis, describing how she both loves and hates him.
O serpent heart, hid with a flow'ring face!
Did ever dragon keep so fair a cave?
Beautiful tyrant! fiend angelical!
Dove-feather'd raven! wolvish-ravening lamb!
Despised substance of divinest show! (Act 3, Scene 2)
Juliet has to pretend that she is not married to Romeo, and she is only sad about Tybalt’s death. She ends up going to Friar Lawrence for help, as Romeo does, but the two cannot talk to each other as easily.
When Romeo finds out he is banished, he is very upset. He says he would rather die than be banished.
Ha, banishment? Be merciful, say ‘death’;
For exile hath more terror in his look,
Much more than death. Do not say ‘banishment. (Act 3, Scene 3)
Romeo wines and cries until Juliet’s nurse arrived, and they make a plan. Juliet is the one, therefore, that takes action. Both are depressed and scared, but Juliet acts before Romeo.