Both Benedick and Othello take a surprising amount of effort to maintain their deliberately-crafted public images. And both of them are ultimately unsuccessful at it by the time the final curtain falls. (The major difference, of course, is that Benedick's reputation is played for laughs, while Othello's is played for tragedy. Oh, and the fact that Benedick's still alive at the end of his play.)
Benedick's image, of course, is that of the love-scoffing cynic. And he puts a lot of effort into it. How do I know he puts a lot of effort into it? Because the man will. Not. Shut. Up. About. It. Look at him whenever Hero and Claudio are around-- it sets him off worse than those fucking anti-pot commercials set me off. He could just make a couple snide comments to himself and walk away--but nooooo, he has to go on and on and on about it--because he's deliberately playing to an audience when he goes off like he does. And that playing-to-an-audience fits right in with what he wants people to think about him. Which brings up the question, Why does Benedick want people to think he's such a crabby ol' cynic? The answer lies in the fact that you can't look down on something unless you're standing above it. Benedick wants people to think that he's too cool and smart to get all gooey and hearts-in-the-eyes over some girl. Of course, the joke ends up being on him, because he and Beatrice are getting all snuggly by Act V anyhow. And does Benedick care that everyone sees right through his facade by then? Of course not-- he's got his own snarky bit of rumpy-pumpy to occupy him.
Othello, though, cares very much that everyone sees right through his image. The image, of course, is that he (a Moor in a European's world) can be a great hero and get the girl and live happily ever after, despite all the disadvantages he faces. In fact, you can sum up most of the play like this:
OTHELLO: I'm a great warrior and I have a beautiful girl to come home to! I'm just as respectable as the rest of you guys!
IAGO: Bros before hos, man. Oh, and speaking of hos, there's a reason why they call her Desdemona The Bicycle...
OTHELLO: OTHELLO SMASH!!!
To put it less flippantly, if people think that Desdemona's playing around on Othello, it means that part of his own reputation becomes a joke. And in order for Othello to occupy that tenuous toehold in respectable society he has, that can't happen. And his efforts to correct it end up ultimately bringing about his own downfall. The stakes of getting seen through are much higher for Othello than for Benedick, which may explain why Othello seems to act more and more irrationally as the play goes on.