Romeo and Paris are both well-heeled young men from good Verona families who wish to marry Juliet. The main difference between them, however, is Romeo's depth of passion and ability to express it.
Romeo is a wordsmith who uses beautiful language to woo Juliet. He never seems to run out of words to praise her. Paris, in contrast, has very little to say to her, even after they are engaged. His speeches add up to little more than
Do not deny to him that you love me
Thy face is mine, and thou hast slandered it.
Not only does Paris not have much to say, his speeches suggest that he is self-centered and believes he owns Juliet. Unlike the passionate and adoring Romeo, he doesn't explain all the ways Juliet's qualities inspire his love and worship. Instead, he is focused on her loving him—and then reminds her that she has slandered him by crying because her face belongs to him as his betrothed. These are not words calculated to win the heart of an emotional and sensitive teenage girl.
It is true that Paris may simply be tongue-tied: few are likely to have Romeo's speaking abilities. At the same time, Paris's self concern doesn't ever seem to extend to real depth of feeling for Juliet. His few speeches are stiff and conventional. Romeo, in contrast, feels love for Juliet to the bottom of his soul so much so that he can't live if living is without her. We can hardly imagine Paris killing himself over losing her, and, in fact, that thought never seems to cross his mind.
Shakespeare takes two young men of a similar class and shows one interested in making a conventional marriage match, the other flinging his heart and soul into the woman of his dreams.
One difference is their birth. While Romeo is a gentleman from a powerful family (the Montagues) in Verona, Paris is related to the Prince (as is Romeo's friend Mercutio). Paris is probably a better marriage prospect for Juliet than Romeo, even discounting the fact that Romeo comes from the blood enemies of her family. Also, the Nurse regards him as a more attractive man than Romeo. She describes him as a "man of wax" and says later that Romeo is a "dishcloth" compared to Paris. Of course this latter quote appears after Romeo's banishment—clearly the Nurse is trying to cheer Juliet up—but he seems to be a more physically attractive man than Romeo.
As for similarities, there are a few. Both appear to be impulsive and impatient, especially when it comes to the prospect of marrying the beautiful young Juliet. Paris is even able to talk Lord Capulet into giving him his daughter's hand in marriage despite her young age. They are both young, and both are clearly in love with Juliet. Obviously this is true of Romeo, but Paris shows up at her crypt to mourn his "sweet flower"—this is how he gets killed by Romeo near the end of the play. Perhaps the most significant similarity between them, though, is that both are plagued with ill fortune. Really Paris as much as Romeo and Juliet is "star-cross'd." After killing the "noble youth," Romeo reaches out to carry him into the mausoleum, inviting the dead man to "give me thy hand / One writ with me in sour misfortune's book."
The County Paris is clearly the marriage material that is sanctioned by Juliet's parents. Romeo, on the other hand, would be killed if he were merely found in Juliet's garden. Paris appeals to Juliet's father, and this would be considered the proper way to approach a woman of Juliet's station if interested in marriage. Romeo, on the other hand, approaches Juliet directly when he develops feelings for her.
I think both do actually care about her, though. In the end, when Paris is at Juliet's tomb and Romeo shows up, Paris fights him in an attempt to protect Juliet's body—he assumes that a member of the Montague family is there to do something nefarious. Romeo fights to die with his wife while Paris fights to protect his fiancee. In the end, both die for the woman they loved in life.
The most obvious similarity is that they are both self-centred. Romeo is more in love with love than he is with either of the women he falls for. Paris is so intent on having Juliet that he doesn't care if he harms her or not. (Capulet, who knows from experience, tells Paris that Juliet is too young and that she hasn't had time to "ripen". Paris responds not by agreeing to wait, but by insisting that girls younger than her have been happily made mothers. Like Romeo, Paris is also so eager to marry that he is willing to rush through without any courtship (another indication that neither of them care very much about the woman--girl--involved). Both Romeo and Paris appear to be or are described as somewhat changeable--Romeo leaps from one girl to the next in a matter of hours and Paris is described as a "man of wax". Being a "man of wax" suggests he may be a superficial beauty without serious substance (of course this assessment does come from the Nurse...)Romeo is also wax-like (unless you see him as changing and becoming solid when he meets Juliet).
As for differences...well, Romeo is young while Paris is old (closer to Juliet's mother's age). Juliet may be almost a bud, Romeo is budding, but Paris is in full bloom, a summer flower. Paris is established and Romeo is not. Paris has Capulet's (eventual) consent while Romeo most certainly does not. Paris is well liked by Juliet's mother and is described as a book to be read and find beauty in while Romeo's only reference to a book is in the way he kisses (by the book).
Romeo and Paris are similar in a great many ways. Both men are presented as potentially adequate suitors for Juliet; both are handsome and well-groomed. They both are of prominent social status, well-connected politically, and have wealth either personally or through their families. While both tend to display streaks of self-absorption and conceitedness, they are also both ultimately men of good character and integrity who prefer the pleasures of love to physical conflict. In fact, both men eschew violence, with Romeo in particular admonishing his cohorts when they seek to fight members of the Capulet family. Unfortunately, both men also meet their ends in the story.
However, Shakespeare also is keen to show the differences between these two men. Their age is of consequence with twenty-five-year-old Paris being nine years teen Romeo’s senior (an even greater disparity at that time when people had shorter life spans). In addition, the disparity in their emotional maturity seems almost a consequence of their age difference, with Romeo far more emotionally reckless and unstable while Paris displays too little emotion. These traits expand into other areas of their personality, with Romeo depicted as fickle, aimless, impetuous—a willing rule-breaker with no job who lets himself succumb to his passions. Paris, on the other hand, is decisive and unwavering, an established and mature working man who has a great respect for the rule of law (as demonstrated when he makes a citizen’s arrest of Romeo at the tomb). But perhaps one of their greatest differences is in how they treat Juliet. While Romeo treats Juliet as his equal and is never possessive of her, Paris can be controlling and often behaves as if he’s her husband even though they are not yet married.
In terms of similarities, both Paris and Romeo have good hearts. They both seem to have genuine feelings for Juliet, and whether or not we believe that they could actually be in love with her, they both feel themselves to be. The fact that Paris goes to the Juliet's vault to strew flowers and weep over her death shows that his feelings are strong and genuine. Then, when Romeo arrives at the grave, Paris confronts him in order to protect Juliet's body, and when Romeo mortally wounds him, he begs Romeo to place his body near Juliet's. Romeo also takes risks for his love of Juliet -- in her garden, in her bedroom -- and his feelings seem sincere as well. The fact that he returns to Verona to die by her side seems evidence enough of the strength of his feelings.
In terms of differences, Romeo seems to enjoy witty wordplay, clever puns, and jokes that rely on sexual innuendo; in other words, he seems fairly intelligent and he enjoys displaying that cleverness, especially with Mercutio. However, Paris doesn't have that same sort of cleverness; he seems a little more innocent, perhaps, than Romeo. The fact that he approaches Lord Capulet for his daughter's hand shows that he tends to play much more according to the rules, while Romeo seems a little less predictable, like he has more of a mischievous side.
There are some obvious similarities between County Paris and Romeo Montague. They are both young men who come from wealthy families; however, Paris is a relative of Prince Escalus, so their social standing is not equal. Both young men are certainly passionate and impulsive. Each of the boys falls in love (or something they believe is love) with Juliet and devotes himself to her without actually knowing her. I would say that the actions of Paris and Romeo show a lack of common sense and maturity. Each of the two is ruled by his emotions.
There are definite differences between County Paris and Romeo. Although Paris does not seem to realize that Juliet is not interested in him, he does take the proper steps necessary to securing her as his wife. Romeo acts in secret and ignores the rules and conventions of society.