Vietnam may have been worse in terms of casualties, but given the changing values of society, I say Iraq did more damage. In the sixties, the last World War I veterans retired, and the country and the economy were run by veterans of World War II and Korea. There was an expectation that the young generation fulfill an obligation to fight “enemies of state,” e.g., communism. The resulting protests changed America for the better: the voting age was lowered, the draft was ultimately eliminated. For decades, the threshold for ground war was raised.
Now, move to Iraq. The invasion began on a false premise of weapons of mass destruction, none of which were found. Saddam may have been a ruthless dictator, and he did indeed oppress the non-Sunni majority. But under his rule, the country functioned and neighbors did not go to war with each other over sectarian issues. By invading, Americans took the blame for civil war in Iraq. Communication is much faster in today’s era, and world opinion over Iraq, in my opinion, is more damaging now than it was after Vietnam. The world sees the US responding to Osama bin Laden and 9/11 by attacking a different country and leader. There is a notion that Bush 43 was trying to “finish” a job his father did not. Add to is the impression of a war on Islam, and America’s world image suffers, not to mention incentives for terrorists.
Eleven years after the Gulf of Tonkin, Vietnam was over. The communists won. As time healed the damage, diplomatic relations with Vietnam would resume. Eleven years after the invasion of Iraq, we have an unstable mess. We don’t know when it will end. Ford and Carter were not burdened by the legacy of Vietnam the way Obama (and his successor) would be burdened by Iraq.
It is true that if Saddam died in 2013, Iraq might have collapsed into civil war anyway. But Americans would not shoulder the whole blame.