How does Romeo's concern differ from Juliet's? What might this comparison reveal about these two characters?

This takes place largely during the famous balcony scene. Juliet is concerned with Romeo's name. Montague is a sworn enemy to her (Capulet) family. 

What's in a name? That which we call a rose

By any other word would smell as sweet.

So Romeo would, were he not Romeo called,

Retain that dear perfection which he owes

Without that title.

Juliet justifies her love for her sworn enemy by saying that there is really nothing of substance in a name. She reasons that Romeo is good husband material despite his last name.