In a European government, the official who would have been announcing his resignation yesterday over the failed hostage rescue mission would have been the equivalent of Defense Secretary Harold Brown, "who thereby would take responsibility for the technical failure. In all likelihood, the British or French Cyrus Vance who questioned the mission's chances would have been in line for a promotion.

The reversed results in Washington suggest not only that America marches to a different diplomatic and electoral drumbeat, but also that much more was involved in Vance's abrupt but predictable resignation than the reasons stated so far. And through their separate stands and responses to the mission's failure, Vance and his opponents within the Carter administration have jointly succeeded in expanding the Iranian confrontation into a global crisis of confidence that requires a sharp turn in American diplomacy now.

Two months ago, one of the most astute ambassadors posted to Washington cabled home that Vance's resignation was an event waiting for the right moment to happen. The diplomat argued that the Soviet invasion of Afghanistan had cut the ground away from Vance and his principal advisers in dealing with their main account, Moscow. Domestically, Vance's handlig of the U.N. Security Council vote on Israeli settlements had made Vance a domestic political liability.

That U.N. vote also demonstrated once again that Vance was not in control of the State Department's own machinery, much less foreign policy, a point that had been made in the Andrew Young-PLO embroglio last summer. Vance had threatened to quit then, and strongly implied earlier that he had come to the edge of resignation over the president's sending Robert Strauss to the Middle East as special negotiator.

But Vance's main role in continuing in a job he had truly grown tired of and despondent over was to project an image of continuity, and of restraint. Allies and friendly nations abroad chose to believe that the crinkly-eyed Wall Street lawyer was constantly wrestling national security adviser Zbigniew Brzezinski and the Pentagon into less bellicose postures. If Vance had resigned because there was a large and punitive military attack planned on Iran as part of the rescue effort, that would be in keeping with the principles he has enunciated in policy meetings.

The fact that continuity and restraint are exactly the qualities America's allies and friends abroad would most like to see in evidence in Washington now raises the question of why Vance chose to abandon Carter publicly at a moment when his presence would still the severe questioning abroad of Carter's intentions.

Moreover, those same circumstances raise another question: why did Carter not make what would have been an irresistible plea to Vance to put the national interest ahead of his own disappointment and lessened authority and stay in the job yet a further time? Vance is not the kind of man who would have rejected such a plea if it had been made.

Vance was not viewed as an effective champion of any particular policy abroad. He has been forced to argue with the president in recent weeks over Vance's desire to resume a dialogue next month with Soviet Foreign Minister Andrei Gromyko in Vienna.

Vance's departure does scramble regional politics in some key areas because it scrambles the widely held perception of his acting as a buffer to Brzezinski's more "globalist" impulses. This is true in Africa, where Young and Vance were personally identified with the policy that helped bring about Robert Mugabe's accession to power in Zimbabwe, and in Asia, where Brzezinski's much harder line on restricting relief for Cambodia could gain the upper hand.

Europe and the Middle East could well switch positions of priority in diplomacy. Carter must now work on restoring some unity to an alliance that he has used - perhaps justly but at considerable cost -- as a smokescreen for the rescue mission. European officials tend to view cabinet resignations as more serious matters than do their American counterparts, and Vance's quitting is sure to be seen as another sign that NATO has been brought to the edge of a major confrontation by Carter's unsteady hand.

The Europeans' rush to voice support this weekend for Carter's actions over Iran empahsizes just how jittery they are about an approaching brink. Carter's actions are seen as truly erratic and dangerous, in contrast to Richard Nixon's calculated unpredictability on bombing Vietnam, a policy that in any event was taken against a background of improving relations with and offering carrots to Moscow to show restraint.

Vance had gained a particular trust from both Arabs and Israelis, and they are likely to see his departure as putting an end to serious efforts in the stalled West Bank autonomy talks before the November elections here. The Middle East may now belong on a back burner, behind restoring confidence in NATO. One of the most likely successors to Vance, Sol Linowitz, has already been singled out by some Arab countries as being politically valuable to Carter at home because he is Jewish, but a liability in pushing Middle East diplomacy now for the same reason. (Henry Kissinger encountered, and broke, this same prejudice, however.)

The more difficult choice thrust on Carter by Vance's resignation involves substituting an emphasis on Europe for the sharp focus he and his aides have chosen for Iran over the past five months. The reaction to the rescue mission and Vance's absence has strengthened the argument from some in Europe that the hostage issue has to be taken out of the spotlight and treated as just another one of the pressing problems facing America abroad. Carter may run the risk of appearing callous to American voters, these Europeans recognize, but they maintain that he runs a far greater risk to American interests abroad by continuing his current policies.