This is not a perfect way of interpreting the play, as I will discuss, but it arrives at a way of understanding the play that is not wrong, because it highlights the Iago-Desdemona-Othello triangle and the tensions pulling Othello apart.
Admittedly, if we interpret the angel/devil motif as something we might see in a cartoon—in which a devil named Iago whispers into one of Othello's ears, and an angel named Desdemona into the other—this is not exactly what happens in Othello.
Iago is the devil who maliciously decides to turn Othello against his wife by convincing him she is having an affair with Cassio. He whispers insinuations to Othello, manipulates events to look like what they are not, and plays on Othello's weaknesses.
Desdemona is an angel who shows her husband love, loyalty, and devotion. That is her way of whispering into his ear: she is true to him, if he could only see it. Because she is such an angel, however, she can't imagine her husband being deceived into turning against her. Because her behavior and mind are pure, she can't imagine that Othello would believe she was having an affair with Cassio. She is still an angel, but an angel whose goodness and honesty put her at a severe disadvantage.
Othello is left with a "devil" and without a wife who knows enough about what is going on to set him straight. We can imagine that if she did know and had been whispering words to counter Iago's, Othello might have believed her. Unfortunately, Othello has to trust her without this reassurance, and, in the end, his own demons of insecurity and jealousy bring him down.
Just because Desdemona doesn't know everything Iago knows doesn't negate her role as angel. It simply puts her at a disadvantage, creating an unequal playing field. Therefore, though Desdemona and Iago can be crudely understood as "angel" and "devil," the two can't be understood as "competing."