Your most idealistic beliefs will be incompatible in a subtle way. You'll both seek personal growth, but after a while it will become clear that you just don't understand each other's methods. You'll naturally be more intellectual about it: You'll actively seek new ideas that you can apply to yourself and your own experiences, and you'll probably read a lot, talk to different people and so on to actively shape your own ways of thinking and growing.
But your friend will take a more passive and intuitive route than that. They'll be more apt to feel their way along, relying on their subtler senses to guide them along their path. Needless to say, these two methods of achieving the same thing will be in conflict with each other unless you're each able to respect your differences.