The Vietnam War started when the Vietnamese people declared independence from a century of French colonial rule. Ho Chi Minh was a widely popular leader, whom over 80% of the Vietnamese people supported, and who had put together a government which had the support of the Vietnamese people. The Vietnamese wanted independence and to be left alone. Vietnam had literally been a slave colony of the French for 100 years, where the native people were slaves in their own land. They wanted freedom, and they wanted to kick all of the foreign powers, who had been exploiting them, out.
After the Vietnamese people had successfully defeated the French, the United States decided to step in to prevent Vietnam from obtaining independence, because of the fact that the vast majority of the people supported Ho Chi Minh who was nominally a Marxist, at a time when the Cold War was at its height.
American involvement in the Vietnam War lasted about ten years, during which the American military killed over one million Vietnamese people, mostly civilians. When the United States finally decided to pull out, the Vietnamese did what they had always intended to do, secure their country and go back to living their lives. No doubt the manner in which this was done would have been much more peaceful and beneficial had they not suffered 15 years of attack from Western powers and had they instead been helped into a transition of independence instead of thwarted at every turn and relentlessly attacked.
The reality is that Ho Chi Minh and his government were always well organized and had the support of the population. The overwhelming majority of the people supported the regime of Ho Chi Minh, which is why they won the war. The only people who really opposed the regime of Ho Chi Minh were those Vietnamese who had ties to French and American interests, and those who had been raised in Catholic missions and taught to fear their non-Christian countrymen. The objective of the Vietnamese in the Vietnam War was, from the beginning, to gain independence, and once the United States left that's exactly what they did. When America left Vietnam order was relatively quickly restored and the Vietnamese people quickly settled-in to mind their own business and take care of their own affairs.
The situation in Iraq, however, is completely different. You see, America could have pulled out of Vietnam at any time, and the worst case scenario was always that Vietnam would "become Communist", however there was never a possibility that there would be a power vacuum, that it would create regional instability, that the country would descend into chaos, that it would become a terrorist state, or that there would be on-going civil war. The war in Vietnam was a war started by the Vietnamese people against foreign occupation. It was a war for independence, much like the American revolutionary war was. America's only role was to try and thwart this process. Failure for America in this war only meant the failure to thrwart the Vietnamese from establishing their own country as they saw fit.
The war in Iraq, however, is completely different. It was started by America, and the conditions in Iraq are such that if/when America pulls out, it is likely that there will be chaos, civil war, and regional instability. The Iraqi people did not ask for this war, America brought it upon them against their will, and America destroyed their country even beyond what had been done to it in the previous Gulf War and by the sanctions. There is no respected authority in Iraq as there was in Vietnam. The likelihood is that in a power vacuum fundamentalist Muslims will take power in Iraq, resulting in a dramatic rollback of progress in the country, and the loss of human rights even beyond what had been the case under Saddam, whereas in Vietnam, when the Communists came to power conditions improved over what they had been historically, though things were obviously not ideal. Women's rights were improved and the slave like conditions under French rule were eliminated. Obviously things could have gone even better, but things certainly did not get worse in Vietnam after the war, they got better.
The point is that, as much as the "quagmire" in Iraq may resemble Vietnam, the situation is really quite different. Vietnam always had a respected leader and government, from prior to the start of the war, throughout the war, and after its end. America could have pulled out at any time and the country would have been fine. America never overturned the Vietnamese government and thus the "nation building" phase never even began in Vietnam. In Iraq, however, the government has been completely crushed and the country is in chaos. Not only is the country in chaos, with no clear Iraqi authority to bring the country under control, but the country is in a particularly sensitive region, with a neighbor who is antagonistic to America and Israel. There is a real possibility that if America pulled out of Iraq, the Iranians would invade. If the Iranians did invade, there would be no way for the Iraqis to defend themselves against it, only the US or a NATO force really has the ability to fend off an Iranian invasion in Iraq. Even if Iran did not invade there is the problem that Iraq could become a real haven for terrorists, illegal activity, and civil war, overflowing into regional wars throughout the region, especially into Syria and Turkey (where the Kurds would likely move the fighting).
So, in reality, the situation in Iraq is much worse that the situation was in Vietnam. There were many more casualties in Vietnam, over 5 million Vietnamese people killed or inquired, and 200,000 Americans killed or inquired, so Vietnam was worse in this sense, but the repercussions of this war are much more grave than those of the Vietnam war. The idea that America can just "bring the troops home" simply doesn't pan out. There is no way to bring the troops home, probably not for at least 10 years. There really is no good solution to this situation. In Vietnam, as I said, pulling out was always an option because Vietnam was always capable of taking care of and governing itself, but Iraq is not and Iraq is in a much more sensitive area to boot.
I believe that America has just gotten into its own Palestinian/Israeli conflict, where there is no way forward, and no way out, at least no way that the people in power will accept, and I suspect that we will be fighting this war or the remnants of it for decades. This not even to mention the fact that the Taliban are taking control in Afghanistan again...
Needless to say, the Bush administration's wars are a true disaster.