There are many points that could be made here, but for the sake of keeping it short, I will look at the main aspects of each man's policies.
- Kennedy's policy was to advise and guide South Vietnam. Under JFK, the US was not very directly involved in the war.
- Under Johnson, the US became much more deeply involved and was trying to win the war on its own. It was under LBJ that US troop levels reached their peak. His only goal was to win the war at any cost.
- Nixon was trying to get out of the war. He gave us "Vietnamization" and the search for "peace with honor." By the time he came to office, Nixon pretty much thought the war could not be won and was not worth it. Most of his actions were aimed at trying to get a decent peace treaty.