You could have a hard time finding common ground. On some level, you'll both recognize that you speak different languages. You might feel frustrated by each other, as if you just don't focus on the same things in life -- and you'll probably be right.
You are different enough that your values and beliefs may not even be complementary. Qualities like stubbornness will be brought to the fore in this friendship. But it can be just as problematic if either of you is the type to maintain harmony at all costs. You could feel as if you're hitting a brick wall when you're trying to communicate, but this could actually be a very positive experience. If you can both learn to step outside yourselves and see things from the other's point of view, you'll learn a lot about life, friendship and communication. You can learn to view each other without judgment.