What a fascinating question! I had never thought of connecting these two texts, before, but now that you mention it I feel that there are definite grounds for a comparison here based on the thematic topic of power. You can think about the way that both the American Dream and Big Brother manage to exert incredible power and influence over people, even though they are concepts and ideas that don't actually exist necessarily.
In The Great Gatsby, for example, there is clear reference to this in the way that the American Dream is shown to exert its somewhat malign influence over characters such as Jay Gatsby. On the one hand it has transformed him into the opulent indivdual that we see presented to us in the text. On the other hand, as the text makes clear, it has sent him in pursuit of an unattainable goal and impossible aims. His death shows the ultimate futility of a life lived in search of the American Dream.
In the same way, in 1984, the ubiquitous figure of Big Brother literally stands over and watches every single character, and the way in which Winston, in spite of his intial rebellion, is cruelly broken and made to love Big Brother by the end of the novel is both cruel and sadistic. Power is something that is centred on this mysterious and threatening figure, and the entire society that we are presented with revolves round this intimidating figure.