This is one of those series that I would have hated if I had read the book first, like was the case for Station 11, which I thought changed a lot of plot points from the book for no narrative payoff. Similarly Man in the High Castle suffers from the chronic media disease of our time: serialization. This is exacerbated also by the decision to change the medium of The Grasshopper Lies Heavy from alternate history novel to apparent newsreels which serves as the first indication that this is multiverse sci-fi rather than straight alternate history. Although this seems to be a common feature of alternate history, since the first alternate history, Bring the Jubilee, as well as the first alternate history that many of my generation read, Guns of the South are both really time travel narratives which cause the timeline's fracture from canonical history.
All this makes the series more of an exercise in world building much more than the tight narrative arc you get in the book. The book never leaves the Pacific States and Rocky Mountains, while the series really delights in showing all of the details of the alternate timeline from American Nazis to the disaffected Lebensborn of Berlin who parallel canonical history's American hippy movement. They even add John Smith, American every-man to delve into American Nazi politics more and display all of the ways fascism tends to devour even its most ardent adherents.
My main gripe, however, is how all of this contributes to mangling PKD's main theme in the book: how arts can force us to imagine different worlds. This is done both kind of explicitly via The Grasshopper Lies Heavy and also more obliquely via Frank's art, which possesses Wu and puts Tagomi into a meditative state where he is transported to canonical America where Japan didn't win the war. We're also forced to consider, since Tagomi, Frank, Juliana, and Hawthorne are all practitioners of the I Ching, that a) the main difference between canonical history and this version might be the veracity of the I Ching and b) Frank and Hawthorne might just be vessels for some other indomitable artistic spirit that yearns for the destruction of fascism.
What it doesn't do is whatever they do at the end of the series with all of the multiverse people. Oh also in the novel the Nazis leave the southeastern US alone out of respect, which is funny and cowardly of Amazon not to include in their adaptation.