There are a lot of similarities between these two ill-fated couples, the first being that they are in fact ill-fated. That means that both of their romances end badly, either in the death of their bodies or souls.
A second similarity is that their loves were forms of rebellion, forbidden in their society at the time. They had to meet in secret, love in secret, and fear discovery at the hands of those who forbade their relationships.
A third similarity is that their initial attraction was mostly physical; Romeo is struck with Juliet's beauty and thinks he is in love. Later, they build on that initial attraction and form a more solid and mature connection. It is the same with Winston and Julia; their first real meeting involves merely a physical encounter; later, they establish an emotional and mental connection.
Differences between these two relationships are that in the case of Winston and Julia, they betray each other and their love in the end; Romeo and Juliet did not, staying true through death. In Romeo and Juliet it was their families who disagreed with the match; with Winston and Juliet it was the government. Romeo and Juliet are much, much younger, young teenagers. Then, Romeo and Juliet's love forged a bond between warring families; the example of their love for each other was so powerful that it changed hearts and lives of many, many people. This is not hte case with Winston and Julia; their story ends more sadly, even though they do not die. Even love wasn't powerful enough to overcome the all-powerful Party; their love for themselves and their own survival trumped their love for each other. Society was not changed by them at all.
I hope those thoughts helped; good luck!