One of the main points of contention that is evident between Barth and Brunner is over the use of philosophy. Brunner had a view toward the world in that he wanted to use philosophy in order to combat various manifestations he thought did not fit within his theology. Sometimes this might be what he called "journalistic" theology or "eristics". It is basically a combative view in the form of using philosophy as apologetics. He believed the prevailing secularism in Europe was a starting point for the church to meet "modern human beings" in their own place and on their own terms.
Barth, on the other hand, thought that theology should have its own space to operate (starting with God's revelation). In short, that one of the problems with theology is when it becomes shaped by a philosophy. Now Barth is often misunderstood at times in thus rejecting philosophy. This he does not do. Here are a few points of what he actually does:
1. There is no such thing as "natural" reason as a first stop before then approaching theology. The point of contact that natural reason is supposedly set up to lead one to the promised land in essence cannot get you anywhere. 2. One should practice the dialectical art of thinking in response to the veiling and unveiling of the event of revelation. This is a continual act because there is no synthesis in Barth's dialectic. 3. Philosophy is to be used as a challenge to theology. We cannot take a triumphalist view toward secular thinkers but should instead listen to what they have to say on their own terms. Much Christian thought, for example, bring out a straw-man Nietzsche or Derrida just to show how bankrupt their thought is in comparison to their theology. If anyone has read Barth, one will see that he learned a lot from atheist/secular thinkers (still, he was not always consistent about this) by listening to their criticisms with open ears.