There is a kind of complementarity between Catholics and Evangelicals today. Very briefly, accepting the authority of the Pope is the key to being a Catholic today. There seems to be little else that unites the bewildering variety of Catholics, from Latin mass hard-liners to Marxist liberation theologians and from the superstitious to the intellectuals.
Accepting the authority of the Bible is the key to being an Evangelical today. There seems to be little else that unites the bewildering variety of Evangelicals, from fundamentalist hard-liners to breezy popularizers and from stuffy traditionalists to laid-back gen-Xers.
Catholics justify the papacy by a hierarchical conception of the church and an emphasis on unity. Evangelicals justify a multiplicity of denominations by a bottom-up conception of the church and an emphasis on doctrinal purity.
Catholics criticize the sola scriptura of Evangelicals by pointing out that a church is needed to determine what is or is not scripture. Evangelicals defend the authority of the Bible by its holy authorship, self-referential integration, and miraculous quality.
Evangelicals criticize the papacy (and the devotion to saints) by pointing out that Christ is our only mediator. Catholics defend the authority of the papacy by its long-running preservation, doctrinal fidelity, and unifying position.
There are two other groups that aren’t part of this complementarity: the Orthodox and the Liberals. The Orthodox are the extreme traditionalists, trying to preserve the church of late antiquity. The Liberals are the extreme accomodationists, trying to be as consistent with larger social and intellectual trends as possible.