This is an excellent question, as actually, there are a number of similarities between these two organizations and the groups behind them. Goldstein is of course the subject of the two minute hate that manages to unite the citizens in Oceania together against him in a hate-fueled frenzy. The novel tells us that he used to be a former member of the Party who rebelled and started his organization, "The Brotherhood," which is explicitly directed towards achieving the destruction of The Party. Big Brother is of course the ubiquitous figure that peers out at the citizens of this dystopian world from every corner.
Although of course these two organizations are ideologically opposed, as one seeks to destroy the other completely, it is clear that the novel deliberately taunts us with the possibility that actually neither of these individuals nor The Brotherhood exists. In fact, O'Brien refuses to answer Winston's question as to whether the Brotherhood exists, only saying:
That, Winston, you will never know. If we choose to set you free when we have finished with you, and if you live to be ninety years old, still you will never learn whether the answer to that question is Yes or No. As long as you live it will be an unsolved riddle in your mind.
The major similarity between these two organizations is the way therefore in which they are sustained and used manipulatively by The Party for their own ends of keeping power and control over the people. Having The Brotherhood with the face of Goldstein behind it seems to unite the citizens for Big Brother and against a common enemy, and this seems to be some kind of psychological necessity that allows the Party to establish and maintain control with its iron fist.