How are Romeo and Mercutio different in Act 1 of Romeo and Juliet?

Mercutio is playful and Romeo is brooding.

Mercutio is a good friend to Romeo.  He tries to cheer him up when he sees that he is brooding over the loss of his girlfriend, Rosaline.  He wants to convince Romeo to go to the Capulet’s party, because he is trying to distract him.  He tries to get Romeo to enjoy himself and possibly find a new girl.

ROMEO

Not I, believe me: you have dancing shoes...

Mercutio is playful and Romeo is brooding.

Mercutio is a good friend to Romeo.  He tries to cheer him up when he sees that he is brooding over the loss of his girlfriend, Rosaline.  He wants to convince Romeo to go to the Capulet’s party, because he is trying to distract him.  He tries to get Romeo to enjoy himself and possibly find a new girl.

ROMEO

Not I, believe me: you have dancing shoes
With nimble soles: I have a soul of lead
So stakes me to the ground I cannot move.

MERCUTIO

You are a lover; borrow Cupid's wings,
And soar with them above a common bound. (Act 1, Scene 4)

Mercutio is able to convince Romeo to go to the party.  There, of course, he meets Juliet.  In the end, Romeo falls in love with Juliet and is very glad that he went to the party.

Mercuito likes to tell jokes.  He engages in playful teasing of Romeo and "locker room talk" about girls. He also gives an impressive speech about Queen Mab and dreams.

The difference between Romeo's and Mercutio's personalies is important because it will lead to Mercutio's death. He teases Tybalt in the marketplace.

Good king of cats, nothing but one of your nine
lives; that I mean to make bold withal, and as you
shall use me hereafter, drybeat the rest of the
eight. Will you pluck your sword out of his pitcher
by the ears? (Act 3, Scene 1)

It is because Mercutio is such a charismatic and playful person that he is not afraid to fight Tybalt.  He has a fiery personality to match Tybalt’s.  Unfortunately, Romeo does not.  He is more complacent and peaceful, and he tries to avoid fighting Tybalt.  As a result, Romeo actually causes Mercutio’s death when he gets in the way.  Mercutio fought to defend Romeo, because Romeo wouldn’t fight, and as a result Tybalt ended up dead.