I think that eventually Kennedy would have had the same type of involvement in Vietnam as did Johnson. The difference might have been that Kennedy may have been able to play to the media better and get more support and commitment to the war.
Clearly the cold war and how both presidents responded are key issues for you to explore. To my mind, one of the most important arenas where we see the effects of their foreign policy is Vietnam, so it is also important to compare and contrast how successful (or not) both presidents were with their approach to this conflict. Certainly it seems as if JFK "wins" if we can use that expression, as Johnson's approach to Vietnam really left the USA in a stranglehold from which it struggled to emerge.
Many historians concentrate on whether or not Kennedy would have gotten us into Vietnam if he had not been assassinated. I tend to believe that he would have, though the timing of our entry and the degree to which we got involved may have been less than it was under Johnson.
Just as JFK was preoccupied with the nuclear standoff between the USSR and the US, and the communist takeover of Cuba, LBJ was preoccupied with Vietnam. They each chose to wage the Cold War in a different way, based on the pressing issues of the moment for them.
I think that one has to examine the role Vietnam played in both administrations. Kennedy certainly got the better end of this sticky situation than Johnson did. Essentially, Johnson's full throttle commitment in Vietnam handicapped him domestically and internationally. Vietnam and the escalation in the region capsized his administration. He was unable to do anything else from a foreign policy point of view because of the complex and intense nature of the conflict. The more Johnson committed, the more unclear the situation became. This had an impact on the rest of his foreign policy, and Johnson became unable to do anything else. Kennedy could be seen in the more explorative stages of the conflict. While he deployed "military advisers" to the region, his commitment was not seen on the same level. Kennedy was able to still have some amount of vagueness in his intentions within the region, to which some attribute a desire to leave it. In the final analysis, Johnson's commitment to Vietnam, where Kennedy lacked it, ended up dooming his administration on multiple levels and crippling his ability to execute a successful foreign policy.
Both presidents found themselves facing the tough challenges of the Cold War. Both presidents struggled to project a strong image of the U.S. to reassure the country's allies that they were on the right side and that the U.S. would protect them from the Communist threat.
One of the major themes of Kennedy's presidential campaign in 1960 was the inability of the Eisenhower administration to secure Third World countries on the American side. To win new allies over to the United States Kennedy based his foreign policy on the concept of nation building and "peaceful revolution" (in contrast to the Soviet leader Khrushchev's idea of "ars of national liberation"). He thought that the United States could help Third World countries and developing nations to build better transport and communication systems as well as to improve agriculture. Kennedy's Alliance for Progress (1961), designed for Latin America, is an example of this strategy. To reach the same aim, Kennedy also created the Peace Corps which would sent educators, scientists, doctors, agronomists to Third World countires. Yet, in spite of the rhetoric of peace that surrounds the Kennedy Administration, Kennedy too relied on military operations and on the strategy of counterinsurgency. This consisted in sending military advisers and special forces to train local troops to repress possible revolutions. America's involvement in Vietnam began to increase greatly during Kennedy's administration which sent to Vietnam more than 16,000 advisers.
Kennedy also relied on the CIA to carry out covert operations against unwelcome regimes: Operation Moongoose in Cuba, the assassination of Congolese President Lumumba, the coup against Brazillian President Joao Goulart and the killing of Vietnamese puppet President Ngo Dinh Diem were all actions carried out by, or with the crucial contribution of, the CIA.
In spite of the escalation in the number of troops and specialists sent to Vietnam by Kennedy, the name of Lyndon Johnson has become indelibly associated with the Vietnam War. Following the doubtful Gulf of Tonkin incident (an event which, as subsequent evidence demostrated, never happened), Johnson succeeded in making Congress pass the Gulf of Tonkin Resolutio, a blank check given to the President "to take all necessary measures to repel any armed attack against the forces of the United States". Members of Congress effectively abdicated all foreign policy in the President's hands. The war soon proved difficult to win and, as it became more and more unpopular at home, Johnson found himself increasingly isolated within his own Administration. Defence Secretary McNamara, once a staunch supporter of the war, resigned in 1968 and the new Secretary Clark Clifford explicitly told the President the war was a "sinkhole". The war also caused a financial crisis due to the massive expenditure required by military operations. On March 31, 1968 Johnson addressed the nation on television to say that he had asked the Vietnamese to begin negotiations. He also announced that he would drop out of the presidential race for 1968.
Johnson, historically, simply picked up where Kennedy left off. Both were in the middle of the Cold War and facing the evolving conflict in Vietnam. They both hotly pursued civil rights and Johnson finished where Kennedy had begun with the Civil Rights Act of 1965.