personally i find this part impossible because in the end their disagreement goes much deeper than mere policy, it is the very character of America. LBJ wants a big Government paradise with constant new programs to meet every need and desire of the American people but also a rock solid admiration for authority and the nation, this means he will still despise the New Left and Anti War movement because in his eyes, they would be ungrateful, ungrateful to the troops defending them abroad, ungrateful for the civil rights and public housing the Government had brought to them, and most of all Ungrateful to him and his fellow legislators who had made it all possible.To him it will be the duty of himself and other legislators to fight this subversive group and continue delivering the Great Society for all with Big government Programs. Pretty soon, with the addition of Evangelical Christians like Billy Graham and possibly blue collar Catholics (this group will be vigorously contested by Kennedy and Co.) to his coaliton, their will also be a social element added to this ideology, a duty to stop the Un American and anti christian hippies which Johnson would happily do (due to his hatred of the Hippie movement in general).
Kennedy is different, he would want a constant questioning of America, new stirring debate to question what he would view as the crushing Machine Likeness of Johnson's America. He would also not be a big fan of Johnsons constant expansion of Government (in many ways he was a predecessor to Clinton style New Democrats at least on Economics) and against the war especially as it grows and grows (although I suspect he will be for it in the begging simply because it was his brother who took the plunge). He will use christian rhetoric too, but not in the Johnsonian way which will emphasise social conservatism, instead using Christian beliefs to better America and to fight Social liberals not with the power of Government (maybe with the exception of Abortion, RFK's devout Catholicism will bring him into conflict with his Social liberal fans on this).