The most evident answer to me is that both of their acts of rebellion fail because they both renounce one another when caught. From this point, one can see that their acts of rebellion end up having the same effect. Renunciation through torture in which the other is sacrificed becomes the sum total of their voice of dissent. They both start out as different. Winston harbors private anger and resentment towards Big Brother, but lacks an outlet to voice his discontent. Julia acts as an agent of the party in her support of abstinence, but secretly enjoys sex. When they both merge, both literally and figurative, it is a realm where private emotions and actions are public resistance. Their relationship is private, but in this condition, it is also highly public. In the end, this is what ends up causing the other to renounce the other. The statement that is derived is that in a government where there is no institutional check or limitation and where encroachment is the modus operandi, resistance and dissent faces an uphill climb and might even result in individual futility.
Julia and Winston both rebel against the Party but act upon their feelings of dissatisfaction differently throughout the novel. Julia finds it exhilarating to have sex with Party members and continuously has secret affairs with various members, including Winston. She is not interested in destroying the institutions, nor is she interested in understanding how the regime controls its citizens. She simply enjoys being rebellious and breaking the rules.
In contrast, Winston harbors deep resentment towards the Party and fantasizes about overthrowing the totalitarian government. He is more concerned with the methods of repression and propaganda that the Party uses to control the population. However, he is hesitant to act upon his feelings out of fear. Winston hopes that one day the proles will awaken and rise up against their oppressors. He is also more interested in joining the Brotherhood in hopes of contributing to the Party's destruction in the future.
Both characters rebel against the Party by carrying on their secret affair and attempting to join the Brotherhood. However, both Winston and Julia are unsuccessful. They are both arrested by the Thought Police and tortured by the authorities.