Juliet's behavior with Romeo, once she has fallen in love, is clearly one of a teenage girl who is smitten. While she was very cautious at first, she quickly falls for Romeo and is full of joy as well as anxiety for the fate of the relationship.
Awaiting the arrival of the nurse with news from Romeo, Juliet is beside herself with anticipation.
The clock struck nine when I did send the Nurse [...]
[...] and from nine till twelve
Is three long hours, yet she is not come. (II.5.1-11)
Like any young girl having to wait for a call or message from her love, Juliet is frantically reasoning in her head why her nurse is taking so long. She left at 9am and promised to be gone a half hour, but it is noon and she has not yet returned. Juliet is worried maybe she could not find him, then tells herself that cannot be true. Her anticipation is very evident upon the return of her nurse as well:
How art thou out of breath when thou hast breath
To say to me that thou art out of breath?(II.5.31-32)
Where is my mother? [...]
How oddly thou repliest! (II.5.57-60)
Throughout the exchange with her nurse, Juliet's temper is growing shorter until she finally exclaims at her nurse "Where is my mother?" as in saying "What are you talking about?!"
On the other hand, Juliet's behavior with Paris can be best described as cordial. Upon first meeting him we see little interaction between the two. Most of the interaction regarding Juliet occurs between Capulet and Paris. Once Juliet finds out she is to marry Paris, her behavior becomes little more than obedience for her parents. She greets him, replies to what he says, albeit she does return smart-aleck answers when Paris attempts to claim her as his own:
Paris: Do not deny to him that you love me.
Juliet: I will confess to you that I love him.
Paris: So will ye, I am sure, that you love me.
Juliet: If I do so, it will be of more price
Being spoken behind your back than to your face. (IV.1.27-29)
The exchange demonstrates Juliet's unwillingness to give Paris any sort of answer or satisfaction regarding her feelings. Paris is already rather possessive since he knows he as good as owns her. However, he does not realize that Juliet is already married, and in her responses you can see her devastation and effort to maintain composure while still telling the complete truth.
Juliet was never smitten with Paris the way she was with Romeo. After Paris leaves the church, she tells Friar Lawrence
O, bid me leap, rather than marry Paris,
From off the battlements of yonder tower... (IV.1.78-79)
Her feelings are clearly ones of desperation. She also shows Friar Lawrence a dagger she has procured to kill herself right then if there is no way out of her marriage to Paris.
At this point Juliet's devotion to Romeo is at much higher levels than when she first met. Again, she demonstrates the passionate levels of attraction that a young girl is likely to feel when she falls for a boy. She never fell for Paris and therefore treated him, at first, only as a possibility because her mother bid her to consider him, and later as a total abomination for interfering in her desire to live happily with Romeo.
Juliet's feelings for Romeo start small and only grow stronger. Her behavior around Romeo is giving and smitten. In his absence her behavior is anxious and willing to do anything to ensure that they can be together. She goes to extremes for Romeo, while she remains at a very lukewarm level with Paris.