Billy Graham was the leading ecumenist and most successful promoter Christian unity of 20th Century. He did far more for ecumenicism than anything coming out of Vatican II or the National Council of Churches.
The NCC promotes dialogue but the organization has never really reached out to conservative or evangelicals Christian churches. Their dialogue is mostly within the context of mainline denominations, actually, often going beyond Christianity and embracing other religions than Christianity.
On the other hand, Billy reached out to the RCC and mainline Christians to promote the gospel of Christ through mass Crusades, while remaining faith to Jesus being the way, the truth and the life and the only way to the Father.
Granted Graham did make a few out of character statements by going overboard in his zeal for unity for which we give him a pass. His son, Franklin, has checked these aberrations of his father in his old age and weakened state of mind. Franklin, for instance, has boldly warned Christians of the dangers of Islam.
Also, the NCC has promoted the concept of social justice, which is a guise for socialism. The organization stands for liberal political and social positions on feminism, environmentalism, disarmament, capital punishment, etc.; while Billy stayed focused on the simple gospel message of the death, burial and resurrection of the Lord Jesus Christ. He counseled both Republican and Democrat presidents.