There are many more contrasts than there are points of comparison between these two “wars.”
The main comparison between the two is that they both are/were very difficult wars to win. This is because neither of these wars could be won in a conventional, military sense. In wars like WWII, it was easy to know how to win. We would simply have to take enough territory from the enemy to make them surrender. But neither the War on Terror nor the Vietnam War could be won in this way. We were not willing to invade North Vietnam and overthrow its government, so our only choice was to try to win the “hearts and minds” of the South Vietnamese. We cannot kill all the potential terrorists in the world so we have to try to get people to feel more positively towards us. In both cases, it is hard to win and it is not even easy to know when we have won.
Outside of that, the two wars are very different. In Vietnam, we fought against a country (North Vietnam) and its agents in the South. In the War on Terror, we are not fighting against any country. In Vietnam, much of the fighting could be done conventionally. We could bomb targets in North Vietnam and we could attack North Vietnamese army units. We have no large targets to bomb in the War on Terror and no enemy units to attack. In Vietnam, we could negotiate for peace with North Vietnam. In the War on Terror, there is no one with whom to negotiate. In Vietnam, once we pulled out, the war was over. If we give up on the War on Terror, it is likely to get worse for us. The North Vietnamese did not want to attack the United States. The terrorists do want to do this.
Thus, we can see that there are similarities between the two “wars.” However, the differences are more numerous and more important.