Did the United States win or lose the Vietnam War?

Depends on how you define "lost" - but the general consensus is that the U.S. did indeed lose.

The U.S. Army reported 58, 177 losses in Vietnam, the South Vietnamese 223, 748. This comes to less than 300,000 losses. The North Vietnamese Army and Viet Cong, however, are said to have lost more than a million soldiers and two million civilians. In terms of body count, the U.S. and South Vietnam won a clear victory. In addition, just about every North Vietnamese offensive was crushed.

Of course, that's not the reason the U.S. lost the war. The American public was outraged that its soldiers were dying, and for what? The government claimed that it was building democracy and infrastructure for South Vietnam. But that couldn't be true, because the U.S. chemical weapon and bombing strategy was ruining the country. If the U.S. was trying to build a new Vietnam, why was it, at the same time, destroying it? Eventually the public couldn't take it anymore, and it almost seemed like mass riots were imminent.

So, it came to be that after losing thousands of soldiers and a ton of cash half a world away on a war for one of the most insignificant places on Earth (in terms of resources and size), the United States of America withdrew its men in uniform because its people said so. Once the U.S. left, the North Vietnamese used their last ounce of strength to push into South Vietnam and win the war. If the U.S. stayed, the North would have definitely lost - but as they say, there is no winner in war.