I think Nixon would have won for the following reasons
1) Kennedy won largely on Looks and charisma, Johnson didn't have that advantage over Nixon
2) LBJs record on civil rights was bad at this point, so he wouldn't have gotten the black vote that JFK did, as well as many northerners might have reluctant to vote for LBJ as well
I also don't think LBJ would have chosen Kennedy, becsause he saw him as a lightwieght and didn't like him.
I would add to that the fact that voter fraud allowed Kennedy to win both Illinois and Texas (on top of the advantage LBJ had there), which if they had gone to Nixon he would have won the EV.