Both are wars in which the U.S. need not have entered and had/have little chance for complete victory or success. The U.S.'s entry into Vietnam was strictly about the attempt to restrict the spread of communism, though there was little chance that it would have directly affected America. Sending troops to Afghanistan at least had a more specific intent: to wipe out Al-Qaeda and halt the world's primary terrorist threat.

In both cases, the superpower went in with the assumption that the country would be eager to change and adopt the governmental style and economic philosophy of the superpower; in both cases, this was a false assumption. Superpowers have a bad habit of thinking that everyone else wants to be like them, which is not the case. We all need to learn to be more respectful of the importance of recognizing the history, culture, and values of other lands and peoples and not be in such a hurry to convert others to our way of doing things.

These wars were quite similar in that both superpowers got in to the wars to prop up governments that were friendly to them.  Both ended up getting stuck trying to support these unpopular governments.  Both lost because they had no way to defeat the enemy militarily because the enemy had too much political support among the people.