The most distinctive thing about Barth’s approach to the doctrine of God is his refusal to apply our conceptions to God – that is, the refusal to start with an idea of, say, omnipotence, or justice or wisdom, and then apply it to God. His reasoning is basically that in doing so, we don’t have God but only our projections of what God should be like based on our own conceptions. That’s the negative side – the positive side is that God determines how God will be known. God’s self-revelation is in Jesus – that’s where we meet, see and know God, and only there.
Another distinctive aspect about Barth is the ‘infinite qualitative distinction’ – there is an unbridgeable ontological gap between man and God (the context for this idea is late 19th/early 20th century liberal Protestantism). Set against the classical tradition, however, there’s more similarity – Barth’s discussion of God’s aseity, self-determination and freedom would be right at home amidst the best of the Scholastics. That God is the unconditioned Being of all beings isn’t something that’s ever been disputed, though again Barth does get there by a different road. I notice some similarities between Barth’s view and, say, David Bentley Hart’s view of God’s (and broadly the classical tradition’s) ‘donation of being’.