When the Illuminatus! trilogy is mentioned, it is usually attached to the name of Robert Anton Wilson, and not to the name of Robert Shea. The conventional wisdom on the matter might be that Wilson's job was to come up with the mind blowing concepts, while Shea's job was the relatively more tame job of turning them into a novel.
Reading the Schrödinger's Cat trilogy pretty much supports the conventional wisdom on this point. While the Illuminatus! presents a rapid fire combination of concepts, characters and overblown plot twists, it manages to also be a well written thriller and mystery novel. The Schrödinger's Cat trilogy, on the other hand, comes across as Robert Anton Wilson's soapbox on his views on mind, society, government and a host of the other usual suspects. The books are written as a series of 1 to 4 page chapters, each a vignette with a short twist or lesson, but without much realistic dialog or character development. The Illuminatus! had some actual character development, while the characters in Schrödinger's Cat are purely farcial or mouthpieces for Wilson's beliefs.
Along with this making the work shallow in a literary sense, the beliefs that Wilson is espousing seem quaint at this point. At first, when Wilson speaks of domesticated primates and neurological metaprogramming, it is entertaining, but soon it comes across as pedantic, heavy-handed and self-righteous. References to quantum physics have not aged well, and neither have the sex scenes, which were perhaps titillating in their day, but now would probably not even be accepted on Literotica. In other words, this book doesn't come off as mind-blowing, at least to me. It comes off as a member of a sub-culture lecturing in a forced style about his beliefs, at great length and with great repetition.