There are areas were his theology would differ significantly from both European and American evangelical theology (for instance his doctrine of election).
Barth started out as you probably are aware studying under some of the leading liberal theologians of the 19th century including Adolf von Harnack, Ernst Troeltsch, and Wilhelm Herrmann (though Herrmann did not consider himself a liberal)
"Herrmann owed much to Schleiermacher, above all, his understanding of faith as a determination of the spiritual life of the Christian that finds expression in doctrines or ideas rather than as a adherence to doctrines of themselves... Herrmann held fast to the conviction that man's coming to his true life depends upon the unique and decisive revelation of God in Jesus Christ. It is not difficult then to see why Barth in 1925 could say that he was not conscious of any 'conversion away from him' but only that he had had to say differently what he learned from him" James D Smart - Divided mind of Modern Theology.
Though Barth later broke with theological liberalism, he never embraced what is probably the key doctrine of american evangelicalism, Biblical inerrancy.
"The problem with which Barth was wrestling...was how to combine an evangelical faith with scientific theological investigation which would make use if the best equipment and the best knowledge available. He had no sympathy with some who solved the problem readily as they entered the pastorate by turning their backs on the academic world, throwing overboard the whole complex of modern theological issues and adapting themselves to their practical situation by conformity with whatever might happen to be the respectable religious standpoint." (Divided mind of modern theology)
"Into this recognised need of "more vital religion" to offset the barreness of Modernism there stepped a man. His name is Karl Barth. Karl Barth had an idea. In some ways it was the most stupendous idea that has ever come from the mind of man. It was a way to reconcile German Higher Criticism and this need of "more vital religion" in the barren Modernist churches....Karl Barth...stated that a thing can be false in history and yet religiously true. To Barth, history doesn't matter...To Barth, the Bible is not the word of God, it just contains the Word of God." Francis Schaeffer - Here We Stand