Winston and Julia are both malcontents; that's about as far as the similarities go. Julia is unhappy because of the restrictions their society places on her, specifically on her sexual activity. She hates the party, but her hatred is more individual, more concerned with herself. Winston, on the other hand, has a more intellectual hatred for the party. He sees it in terms of more than himself, and he seeks to destroy it not only in his personal life, but through helping to foment the Goldstein rebellion.
We see this most clearly in the scene in the "upper room" where Julia and Winston are in bed, perhaps after just having sex (Julia's rebellion), where Winston (the one who traditionally would have rolled over and gone to sleep) is up, reading the intellection content of Goldstein's book, and Julia, bored with the whole thing, is sleeping.
It doesn't really make any difference in the end; all malcontents come to the same end.
Don't you wish Orwell had included a section on what they did to Julia? Different book. :)