In the scholarly study of the Vietnam War in the United States, the two claims you mention were some of the central questions until recently. While there is no doubt that the United States lost the Vietnam War (that is, they failed to achieve the objectives they set out), the question of whether or not it was a strictly militarily or strictly political (or why not both?) has been debated since the end of the war. As I've described in this extensive post of the development of the historiography of the war, there is no easy answer to this question and in fact, academic scholarship has moved away from them, seeing them as rooted in now irrelevant ideas of what was considered important to focus on.