Can we make a comparison between Shakespeare's Julius Caesar and Othello? What are the differences and the similarities?

You absolutely can compare Julius Caesar with Othello. The two plays are both tragedies, so they share many similarities. Both focus on tragic heroes (Brutus in Julius Caesar and Othello in Othello) who meet their end when external forces exploit their weaknesses. Brutus, for instance, allows his sense of honor to blind him to the cruel reality of politics, while Iago uses Othello's tendency to be jealous to destroy him. Thus, at a very basic level, the two plays have similar structures and focus on similarly tragic heroes. 

Although there are similarities between the two plays, there are also many differences. Julius Caesar, for instance, is a sweeping investigation of political scheming, the value of freedom and representational government, personal codes of honor, and the power of mob mentality. It is, in other words, a sprawling and epic look at the nature of government and the perils of trying to correct a corrupt system. Othello, on the other hand, is much more tightly constructed, as it focuses almost completely on Othello's relationship with Desdemona and Iago's efforts to destroy it. The play focuses on domestic themes, such as infidelity and jealousy, and it largely avoids tackling the public world of politics. As such, if both plays are similarly tragic, then they approach their tragic subject matter very differently, as Julius Caesar opts for epic political drama, while Othello examines the much more intimate world of relationships.