Both characters are prime examples of "tragic heroes". Both fall from a high status to disaster. Their social standings are still very different. Julius Caesar is, well, the leader of Rome. Othello is a Moor, and therefor still looked down on by some. Another way to compare and contrast the two is to consider how they treat the women in their life. Caesar has at least some respect for his wife, while Othello ends up murdering his out of jealously.
Each of the men is something of an enigma to the reader in that we are unsure of the reality of thier granduer. By this I mean that each man is part creation of the state (the esteem in which they are held) and their own mind. Each holds themselves infallible, yet each is worked on by minds greater than their own. JC is worked on by Cassius and his band of conspirators as they call into question Calpurnia's dreams and suspicions and the words of the soothsayer. JC, part creation of the state and a certifiable god of war through experience, believes his own press and will not be subject to the fancies of fate, much less a woman. Othello, similarly, is undone by his intellectual superior in Iago. While Caesar underestimates those who seek not to be ruled by a mere mortal, Othello overestimates the affection claimed by Iago. As his ensign, Iago risks his life in battle to protect Othello's colors which engenders a perceived loyalty between the men, which is true on Othello's part, but feigned on Iago's. Othello is bound completely by the loyalty that cannot be matched in a marriage relationship to Desdemona. So, while JC is pride incarnate, it seems that Othello is loyalty. Only Othello's loyalty lies in the wrong place, which is his undoing. Each of the men also seem to believe in own inherent worth and singular skill set that make them irreplaceable in their own minds, with one being on a grander scale than the others.