Paris is a young Count, a nobleman with a title, that is seeking to marry Juliet. At no point does he try to woo or even consider her emotions, he sees their union as no more than another part of his career as a nobleman. When Paris faces off against Romeo in the tomb, he does so out of the pride of what belongs to him and the honor in defending the house of his fiancee.
In contrast, Romeo has no interest in titles or the career as a nobleman. To him, the trivialities of the English aristocracy are useless, he aims for something larger. While his intentions are rather good, he still is "wet behind the ears" and is often immature about his actions, completely forsaking his friends and family for the idea of love and its purity. His way of going after Juliet is fully in consideration of her emotions and wooing her, he takes the time to say the right things and doesn't just expect her to fall head over heels for him like some men of that era did.
Basically, you have a contrast of two different sides of a ridiculous outlook being portrayed by Shakespeare. You have the aristocratic man that feels he's indebted to a young and beautiful bride as a showcase to his career and another notch in his accomplishments, and you have the amorous Romeo who, in his immaturity, has high expectations of love and goes about being the poetic lover, something that was over used and over done during that era. Both end up being a mockery of what a true relationship should be about. One without romance and one overly romanticized.
