Stanley Cutler says that "of all the presidents in the last 50 years, it is Nixon that’s the most interesting." Is Nixon more interesting than LBJ? I'm not sure. I would say, however, that I find Nixon, Johnson, and Reagan to be the most fascinating postwar presidents.
Which suggests a theory of interesting presidents: the partisan presidency makes for less interesting presidents. Generally, the partisan presidency began to form as early as the Carter years, but really didn't pick up steam until the Reagan administration; it's pretty much fully formed, I would say, by George H.W. Bush's presidency.
The idea would be that partisan presidencies are much less likely to take on the shape of the president's personality. So Barack Obama or George W. Bush might be just as inherently interesting as John F. Kennedy or Jimmy Carter, but it just doesn't matter as much; what they do as president is much more a function of party than presidential personality.
To be sure: even now, personality (and skills, and other president-specific traits) certainly can matter. But less so, perhaps, than they did when party was less important.
Is this theory correct? I have no idea. Reagan doesn't quite fit. And it's certainly very possible that my sense of the presidents who are interesting is highly subjective -- or, that it might be influenced by other things that have nothing to do with party. It's certainly also possible that the three I find most interesting really are, in some sense, the most interesting -- but that it's just random luck that two of them served during the peak of the personal presidency.
So, who do you think were the most interesting postwar presidents?