What does America think it has as responsibilities to those who served in wars generally? How does the Vietnam War differ, or does it?
In general, the United States has, since the Revolutionary War, provided various types of benefits to honorably discharged veterans and those who are wounded. I say "various" because, over the course of several wars, benefits have increased as the nation has become more conscious of what sacrifices are made by its military personnel and how best to compensate them for those sacrifices. The Veteran's Administration oversees the implementation of benefits and is the veteran's point of contact for all such benefits.
For example, in 1940, the Soldier's and Sailor's Civil Relief Act (now, revised as the Servicemember's Relief Act) provided certain civil benefits, such as relief from civil suits, debt collection, foreclosure (among others) while someone was (or is) on active duty. In addition, the G. I. Bill provides, among other things, veterans the ability to attend college and trade schools, with the government bearing most of the expense. Another responsibility carried out by the government is to care for veterans who have service-related health problems, but it is important to understand that, currently, health coverage for veterans encompasses only those health problems attributable to active service. If a veteran cannot document that a particular health issue is related to his or her service, the problem is usually the veteran's to resolve.
As to your question about veterans of the Vietnam War, the answer is that veterans of any war are entitled to benefits in effect during their time of service. But implicit in your question, of course, is whether the popularity of a particular war has any effect on veteran's benefits, and the answer is a qualified "Yes." Because the Vietnam War is perhaps the most highly-politicized and unpopular war in 20thC. American history, its veterans felt (and feel) that unpopularity. When people came home from Vietnam, for example, often their first goal was to get rid of their military identity and move forward as if they were never in Vietnam. I don't mean to suggest that they were ashamed but rather that they wanted to move back into the civilian population with the least amount of trouble. In other words, identifying yourself as a Vietnam Vet often brought derision rather than thanks, especially if you were going back to school, so the practical thing to do was to not advertise veteran's status. This is a long way of saying that many veterans of the Vietnam War were often reluctant to use all of their veterans benefits, especially if using those benefits brought attention to the fact that they were veterans.
From an administrative standpoint, however, the US willingly provided substantial veterans' benefits to Vietnam veterans. The issue was always whether or not a particular veteran wanted, in the face of such an unpopular war, to advertise his or her participation.