You'll find that you're at odds in the ways you think, communicate and approach life in general. You're just such different people, with personality traits that will seem to be in conflict. It's likely that you'll both be more attuned to the differences between you and to the qualities you don't like in one another than you are to your similarities or to the qualities in one another that you respect or appreciate.
This is simply a natural, if unfortunate, focus for you two. However, a friendship between you could have an overall positive effect -- it could force you to examine your own natures and make conscious changes in the ways you meet the world.