We aren't told a great deal about Paris, but we are told enough to see that there are both similarities and differences between he and Romeo.
For one thing, we know that both are very handsome men. In fact, if we can believe Nurse's opinion, Paris may even be more handsome than Romeo. We learn about Paris's physical appearance early on in the very first act. Both Lady Capulet and Nurse praise Paris's looks when in the third scene Lady Capulet is trying to persuade Juliet to think of marrying Paris. Nurse describes him as a "man of wax," which literally refers to a wax statue and is to say that he has very statuesque, or beautiful, looks (I.iii.80). Even Lady Capulet comments, "Verona's summer hath not such a flower," meaning that nothing in Verona, not even a flower, is more beautiful than Paris (81). Later in the play when Juliet must choose between her husband Romeo and Paris, Nurse even says that Romeo can't compare to Paris, as we see in her line, "Romeo's a dischclout to him" (III.v.229).
We also know that Paris is a much more sophisticated and possibly even more reasonable man than Romeo. We learn in the very second scene that Paris has been pursuing Juliet's hand in marriage for apparently quite some time now. But each time, like a reasonable man, he accepts her father's decision and resolves to try again later. Romeo, on the other hand, won't really accept "no" for an answer, but instead endangers his own life by jumping into the Capulets' garden for a chance to see Juliet again, maybe even in hopes of seducing her. We even learn in the very first scene that he has so unwisely allowed his emotions over Rosaline's rejection to control him to the point that he stands outside all night long crying. Hence we see that Paris has much more rational and controlled emotional responses, while Romeo does not.