I think that one striking similarity between both works is the construction of the main character. That which is not real provides the essential fuel for both Gatsby and Othello. Gatsby's being is driven by a belief that is not real. His dream of Daisy is built on a "fairy's wing." It is not rooted in reality. It is driven by the aspirations in his mind. That which is not real is what drives Gatsby. In much the same way, Othello is animated by Iago's lies. The deception that Iago weaves is what drives Othello to believe the very worst about Desdemona and Cassio. Othello's fuel to uncover Desdemona's unfaithfulness is what motivates him and compels him. In both conditions, the protagonist of each narrative is fueled by a construction of reality that is not real.
This condition helps to illuminate another similarity between both protagonists. There is a refusal to confront reality in both Gatsby and Othello. For both men, an honest discussion, an open discourse, and a sober view of reality could help to avert the tragic conditions of each. Both men refuse to examine reality and embrace a condition that is either Romantic or conditional. Othello and Gatsby have so many attributes and demonstrate so much that is good. Yet, their inability to discuss their own lives and pursuits in an open and honest manner is what consigns them to failure and doom.