Your minds go off in very different directions and you'll probably end up looking at your friend as a stranger -- and not an interesting or compelling one. In the early stages of your friendship, you might enjoy these mental differences, because they'll seem new and intriguing. But after some time, you'll realize that your ideas are often incompatible.
This person is more intuitive than you are, while you tend to rely more on logic. Neither of you is inherently smarter or a more reliable thinker than the other, but you'll both spend time trying to prove that your point of view is, in fact, the more valid one. At base, you'll be uncomfortable with your friend's leaps of faith and unorthodox ideas, and they'll be impatient with what they'll see as your stodgy, unimaginative approach to the world. You'll have to strike a balance if you want to get along, which means respecting each other's way of doing it.