There is no one single American experience in the Vietnam War. The experience of Americans depended on whether they were in combat in the war, whether they were in Vietnam voluntarily, when they were in Vietnam, or even (if we take the idea of “in the Vietnam War” more broadly) whether they were even in Vietnam.
For soldiers in Vietnam, the experience could differ greatly. An American who was there as a volunteer in the earlier days of the war would likely not have had such a negative experience. That is not to say that war is ever pleasant, but this soldier would have been likely to be much less unhappy than a soldier who was drafted late in the war when American public opinion had turned against the war. Such a soldier would have felt much more futility and anger about being in Vietnam.
Back in the United States, experiences would have varied widely. The experience of a protestor who was trying to evade the draft would have been very much different than the experience of a World War II veteran who supported the war. For all Americans, it would have seemed at times that the war was pulling the country apart. Beyond that, however, there would have been Americans whose experiences were almost completely different.
Thus, it is impossible to talk about any one “American experience in the Vietnam War.”