How is Romeo's view of punishment different than Friar Lawrence's?

Romeo and Friar Lawrence disagree about the fairness of Romeo’s punishment for killing Juliet’s cousin Tybalt in Act 3, scene 3 of Romeo and Juliet.
At the beginning of the scene, the Friar returns to his cell where Romeo has been hiding out to give him news of Prince Escalus’s verdict: Romeo will be banished from Verona. Friar Lawrence is relieved that the punishment is only banishment when the Prince could easily have called for Romeo’s death. He sees this ruling as the Prince showing mercy and counsels Romeo to look on the bright side, saying, “Be patient, for the world is broad and wide.”
Romeo strongly disagrees, protesting that, “There is no world without Verona walls/But purgatory, torture, hell itself.” Romeo’s view of his punishment is different from Friar Lawrence’s in that his first thought on hearing the ruling is that being banished from Verona is the same thing as being banished from Juliet’s side, saying:

“Tis torture, and not mercy: heaven is here,
Where Juliet lives; and every cat and dog
And little mouse, every unworthy thing,
Live here in heaven and may look on her;
But Romeo may not: more validity,
More honourable state, more courtship lives
In carrion-flies than Romeo”

Friar Lawrence is relieved Romeo will be allowed to live, but in these lines, Romeo makes it clear that he considers being alive but unable to be with the one he loves to be a fate worse than death. The knowledge that others, even varmints like mice and flies, are allowed to be close to Juliet while Romeo is exiled is torturous, so in the Prince's ruling he sees cruelty, not mercy. His reaction is so extreme partly because Romeo and Juliet have only just been married and have not yet even had the chance to spend the night together, so the idea of being separated from her so soon is especially upsetting.
Romeo’s heightened emotional state is evidenced in the text by his many exclamations and his use of violent metaphor, telling the Friar he “cutt'st my head off with a golden axe,/And smilest upon the stroke that murders me.”
In response to Romeo’s ranting, the Friar calls him a “madman” and tries to get him to listen to reason, saying, "this is dear mercy, and thou seest it not." His advice in this scene reflects the friar’s role as an older, wiser presence in Romeo’s life throughout the play, urging impulsive young Romeo to have some perspective and to think before he acts. Their difference of opinion about Romeo's punishment is a perfect incapsulation of their characters: Friar Lawrence reacts rationally; Romeo reacts emotionally.
Halfway through the scene, Juliet’s Nurse arrives with news of Juliet’s despair at hearing of her cousin’s death and her husband’s banishment. When he learns of his wife’s unhappiness, Romeo reaches the height of his desperation. He draws his sword and threatens to take his own life, foreshadowing the events of the end of the play. To stop him, Friar Lawrence delivers an impassioned speech, finally driving his points home to Romeo and getting him to listen by laying out a definitive plan of action:

“For then thou canst not pass to Mantua;
Where thou shalt live, till we can find a time
To blaze your marriage, reconcile your friends,
Beg pardon of the prince, and call thee back
With twenty hundred thousand times more joy
Than thou went'st forth in lamentation.”

Friar Lawrence’s point here is the same as it was in the beginning of the scene when he told Romeo “the world is broad and wide,” namely that as long as Romeo is still alive he still has time to fix things, whereas if he were dead there would be no hope at all.
Though Romeo is still unhappy about being banished, by the end of the scene he agrees to the Friar’s plan and seems to have come around to his way of thinking about his punishment.

It's act 3, scene 3 in Romeo and Juliet. Friar Lawrence brings Romeo the news that he's been banished from Verona by the Prince for killing Tybalt. The Friar appears somewhat relieved that Romeo hasn't been condemned to death, which would be the normal punishment for such a heinous crime:

A gentler judgment vanished from his lips:
Not body’s death, but body’s banishment.

But Romeo is having none of this. As far as he's concerned, exile is a much worse punishment than death. For if he were dead, then at least he could be with Juliet:


Ha, banishment! Be merciful, say “death,”
For exile hath more terror in his look,
Much more than death. Do not say “banishment.”



Verona is all Romeo knows. It's where he was born and raised; it's where his family lives; and, most importantly of all, it's home to his beloved Juliet. To be banished from Verona is truly a fate worse than death for Romeo:


There is no world without Verona walls
But purgatory, torture, hell itself.
Hence “banishèd” is banished from the world,
And world’s exile is death.



Friar Lawrence is older and wiser, however. He cannot believe that Romeo could be so ungrateful at this display of gracious mercy by the Prince. Romeo has had a very lucky escape and the Friar is incredulous that the young man doesn't realize this:


O deadly sin! O rude unthankfulness!
Thy fault our law calls death, but the kind Prince,
Taking thy part, hath rushed aside the law,
And turned that black word “death” to “banishment.”
This is dear mercy, and thou seest it not.