You find that you're somewhat at odds in terms of the images you try to project to the world. As a couple, you work at cross-purposes -- you want to seem sophisticated, erudite, while your partner wants to fly in the face of all the stereotypes those qualities imply. Their rough-around-the-edges charm goes directly against your streamlined exterior.
While you might not fight about these differences in a very serious way, you both notice them -- and you both feel rebellious against the other's way of doing things. You might even try to control each other's behavior, to make each other become the kind of lover you wish you had. These differences are merely external, so why not just enjoy them? If it's public opinion you're worried about, you might as well forget about it. You'll never be able to please everyone, after all; so pleasing yourselves could be the best way to go. Your external differences could even be part of your attraction for each other. Together you make up two different halves of a whole, and there's nothing wrong with that, though convincing either one of you of that fact could be pretty difficult! Instead of allowing yourself to treat your partner as an embarrassment, you should try to be brave and appreciate the spice that they bring to any given situation.