This is a subjective question, and different readers are going to answer the question in different ways. Ultimately, the person asking this question is likely more interested in your ability to make a decision and support it with evidence. Personally, I think it is probably easier to defend Juliet being the stronger character.
Romeo comes across as a weak character right from the beginning of the play. He is presented to readers as a Petrarchan lover, and I tend to believe that Shakespeare uses Romeo to make fun of this kind of person. Romeo is in love with the idea of being in love, and when a woman doesn't reciprocate his advances of affection, he falls apart and wallows in his own misery. You could pick just about any quote from Romeo's opening scene for evidence of just how over-the-top his overreaction to Rosaline is:
Tut, I have lost myself; I am not here;
This is not Romeo, he's some other where. (1.1.188–189)
To be fair, Juliet is just as infatuated with Romeo, but her falling in love is more of a departure and change from the Juliet that we were first introduced to. When readers are first shown Juliet, she isn't swooning and in need of love, but is hesitant at the idea of having to marry anyone. Her parents desire her to have a wealthy and powerful husband, but Juliet pushes back against her parents wishes. Her mother encourages her to look at Paris with an open mind, but Juliet is strong enough to not fully honor that request. Juliet appears to have a mind of her own that she is in control of rather than always being controlled by emotions like Romeo.
I'll look to like, if looking liking move:
But no more deep will I endart mine eye
Than your consent gives strength to make it fly. (1.3.99–101)
Therefore, one could argue that Juliet is a stronger character because she maintains her free will and agency despite her parents' wishes and does what she wants to do despite the constraints of her circumstances.