So the crux of this question is what makes someone a historian, and what makes a work a work of history? (n.b. the criticism of GGS is less that Diamond is not a historian, but that he does not apply sound historical method to his attempt to explain societal differences. More on that below.)

By many people's standard, Caro is not a historian -- his undergraduate degree from Princeton is in English, and he enrolled briefly in a Rutgers English PhD program before beginning work as a journalist. After leaving that program, he worked as an investigative reporter for Newsday -- he had been the editor of Princeton's newspaper -- and became interested in how people use power, and the limits of it, when writing a piece on Robert Moses' plans to build a bridge across Long Island Sound. There's a semi-famous quote of his that I will paraphrase, as I can't find it offhand, along the lines of "people think bridges get built due to traffic flow and density concerns, but they actually get built because Robert Moses wants them built."

When he was awarded a Nieman fellowship at Harvard (the Nieman fellows/Nieman reports are journalism focused), he began work on a biography of Moses, which was published in 1974. Subsequently, his focus turned to LBJ, and he has written four of what's planned to be a five-volume series on Johnson (and may the Maker preserve him until he completes it). He's done that as an independent researcher, and he also writes for some popular magazines &c, but his man research project is his LBJ series.

OK, so, but is he a historian?

Let's back up to the fact that he's an English major working as a journalist. I tend to take the view that what makes someone a journalist is not necessarily formal journalism education, but a dedication to the craft of journalism -- if you write journalism, do you draw on a wide variety of sources? do you make sure the stakeholders in a story are fairly represented? do you fact check your sources (if your mother says she loves you, check it out)? do you attempt as much as possible to be fair and accurate in presenting a story? -- well, if you do those things, you're applying journalistic method to your work and you're a journalist, whether you're writing for the Gray Lady or your own blog in your mom's basement.

Similarly, to evaluate Caro's chops as a historian, what we can do is to look at his work and evaluate how it comports with sound historical method. Caro has spent more time in the LBJ archives, since the mid-1970s, than likely anyone else on earth; he cites his sources (looking at you, Shelby Foote); his textual criticism is spot-on; he explains his reasoning for choosing between conflicting narratives; he has mixed archival work with in-person interviews with people who worked with Johnson; and, again, he cites his sources, so you can go back and look at them yourself.

If he's applying sound historical method soundly, then yes, I'd say he has some chops as a historian.

But what about the books themselves? One thing to keep in mind is that they are written from a point of view (as all books are, of course -- there is no such thing as an unbiased work). They are written extremely well and are engaging, something that not all historians can achieve (looking at you, Charles Sellers. Gah.) He clearly dislikes Johnson as a person, while being interested in his story and the stories of those around him. He has come in for criticism before with regard to his treatment of Johnson's many mistresses, the way in which his narrative focuses on Johnson and elides other actors, the idea that his first three books were too hard on Johnson and the fourth too easy, the whole question of writing Great Man history, and so forth.

Some of those criticisms, I think, are fair -- of the top of my head, his account of the 1948 Senate race between Johnson and Coke Stevenson, Caro idealizes Stevenson as a vintage Texan, last of the cowboy heroes, while glossing over Stevenson's racism and reactionary conservatism (though maybe that's implied by being a cowboy hero) -- he works very hard to contrast the principled Stevenson with the money-grubbing Johnson. And to be fair, Johnson won that election by stuffing ballot boxes in the border counties.

Some are not, in my opinion -- Johnson does seem to have risen well above himself managing the transition of power after Kennedy's assassination, inheriting a cabinet that cordially (or not cordially in RFK's instance) hated him. But many of the flaws above are flaws that are inherent in biography, focusing as it does on the individual and how they affected the people around them -- the lens only captures what's in its immediate view.

Is the series the only book you should read on Johnson? Of course not. But does it do a fascinating job of presenting his life and times? Yes.