There's a certain magic to Kennedy in the primaries. There'd be a mythology and nostalgia, but it would be different, and would focus on those tentative months of his campaign, what he offered, and the potential for the future we would have seen going forward from 1959 to 1960.
The important distinction between Johnson and Kennedy is lack of nuance. Distinct personalities would govern the White House. Kennedy was more nuanced, and was a balanced intellectual who would refer to his cabinet and advisers, and if he didn't agree, he would debate them into submission. Johnson was cruder, and had a governing view that you took a switch and whipped things into going your way. We could have had direct troop intervention in Vietnam in 1961; the cabinet thought that we had to send in the troops then and there to fight the Communists, and there was no avoiding it. Kennedy said no, and increased advisers. Johnson may have said yes. Johnson may have sent troops into Laos, which is another war Kennedy avoided. Johnson may have let the troops go right up to the border with East Berlin; when that happened in the OTL, Kennedy was furious that the general had made that decision on his own because he thought the president would have wanted it, and forced them to back off. Johnson may have wanted it -- eye to eye with the Soviets to show them strength and resolve. I do feel it is in Johnson's personality to take one of those incidences, and turn it into a war: whether it be Laos, Vietnam, Cuba, and lord help us if it's Berlin. I think Johnson would be forced to have a cooler head because of the potential for WW3 there, but it could evolve into a bigger crisis.
From a legislative perspective, I would not assume mcguffin LBJ who passes the Civil Rights Act of 1961 and starts the Great Society 4 years earlier. The legislation took an agreeable Congress to pass, and a lion's share of the fighting for the Liberalism of the 1960s was done by Senators. One can't forget that when Kennedy died, Johnson did try to pass the Civil Rights Act earlier, and it failed. It took the Liberal congressional gains after the 1964 election to put in place a legislature that moved in that direction. Once Republicans made major gains in 1966, Johnson ran into difficulty getting things passed and got caught in gridlock, because as he admitted himself, he needed a legislature that would work with him. Johnson here would be dealing with a 1960 Congress -- the same one that deadlocked Kennedy.