To begin with, Stewart is an excellent writer. This is a topic I already find interesting, but I think that he does an admirable job making something esoteric profoundly interesting and, above all, human. He takes to heart the Nietzschean maxim he cites that philosophies are merely expressions of the temperaments of their creators; the story he tells is more about the men and the times in which they lived than their ideas.
What little is known of Spinoza's life is something I'm already familiar with, but I knew next to nothing about Leibniz. Stewart's analysis of the two figures is perhaps a bit too neat to be accurate, but it makes for a wonderful account that is not totally implausible.
I find it difficult to determine which philosopher he sides with. More of the book is devoted to Leibniz (in part because he lived so much longer) but Leibniz characterized as a reaction to Spinoza.
In terms of the exposition of the two thinkers' philosophies, Stewart does an admirable job for a popular work. I can speak less for Leibniz, but on many of the most important points, he gets Spinoza right. He rightly recognizes Spinoza primarily as an ethical and political thinker (so too, Leibniz, for which he provides evidence ample enough to convince me at least).
He uses a few turns of phrase I don't care for: e.g., he talks about Spinoza's "parallelism" while simultaneously describing it as distinctly not that (unless a single line can be parallel to itself). Extension and thought are two aspects of the same nature, and he clearly understands this, so in what sense is this "parallel"? To me that seems a better epithet for something like Malebranche's fantastical "occasionalism" or even Leibniz's "preestablished harmony". He also follows Shirley in rendering what is better translated as "joy" and "sorrow" into the unduly austere terms "pleasure" and "pain".
The way he connects the two philosophers to two fundamentally different reactions to modernity is compelling, if a bit overstated. While throughout the work he is trying to argue for a greater than recognized influence of Spinoza (albeit a negative one) on Leibniz, his own thinking really comes to the fore in the closing chapter. I love the way that he unapologetically lumps Heidegger and the Postmodernists into the same camp as Kant and Hegel, essentially imitators of Leibniz's reactionary stance. It is by no means fair to these thinkers, but it is certainly amusing to imagine the reactions of their contemporary proponents.
He also makes a solid case for my suspicion that Locke is largely a hack who stole Spinoza's ideas without crediting him because he was too controversial. And in a few short paragraphs he demolishes the established practice of calling Spinoza and Leibniz, along with Descartes, "rationalists".
Do I regard Spinoza as a champion of modernity, as Stewart clearly maintains? I suppose it depends on what we understand by modernity, but Spinoza undoubtedly embodies many of the greatest values of the Enlightenment and was a thinker centuries ahead of his time. The world that we live in now, I think, is constituted largely by this struggle between the proponents of a secular society and a great hodgepodge of reactionary forces. On this note, Stewart's closing passages are particularly apt (the bracketed insertions are my own, obviously):
Leibniz was a man whose failings were writ as large as his outsized virtues. Yet it was his greed, his vanity, and above all, his insatiable, all too human neediness that made his work so emblematic for the species. With the promise that the cruel surface of experience conceals a most pleasing and beautiful truth, a world in which everything happens for a reason and all is for the best, the glamorous courtier of Hanover made himself into the philosopher of the common man. [What audacity! To claim a thinker so abstruse as Leibniz to be "of the common man" is obscene. I love it!] If Spinoza was the first great thinker of the modern era, then perhaps Leibniz should count as its first human being.
Spinoza, on the other hand, was marked from the start as a rara avis. [Philosophers cannot resist showing off their familiarity with dead languages even in purportedly popular works.] Given his eerie self-sufficiency, his inhuman virtue, and his contempt for the multitudes, it could not have been otherwise. [I think this is a bit overstated, and partially a product of our lack of knowledge about the circumstances of Spinoza's life.] Yet the message of his philosophy is not that we know all that there is to know; but rather that there is nothing that cannot be known. Spinoza's teaching is that there is no unfathomable mystery in the world; no other-world accessible only through revelation or epiphany; no hidden power capable of judging or affirming us; no secret truth about everything. There is instead only the slow and steady accumulation of many small truths; and the most important of these is that we need expect nothing more in order to find happiness in this world. His is a philosophy for philosophers, who are as uncommon now as they have always been. [An obvious allusion to Spinoza's final thought in the Ethics: "all things excellent are as difficult as they are rare". I take this as evidence that he ultimately favors Spinoza, but I'm not always so sure.]
In contrast to the suggestion of this poetic denouement, I recommend Stewart's book to philosophers and non-philosophers alike. Finding decent popular accounts of Spinoza's philosophy is nearly impossible, and while Stewart has his flaws, the beauty of the historical narrative alone makes it worth reading. To everyone (and I know there are so many of you who read this) curious to understand what I find so remarkable about Spinoza, this is not a bad place to start.