A couple years went by between my reading the first book in this series and getting my hands on the second, but given how little the characters and events in this book overlap with the first, it really doesn't matter.
Where the first book followed Daniel Waterhouse, Natural Philosopher and scion of a staunch, politically active Puritan family, and took place mostly in England, this book follows "Half-Cocked" Jack Shaftoe (whose nickname refers as much to an anatomical peculiarity of his as it does to his spontaneous and intemperate disposition) and a mysterious, beautiful and very clever woman named Eliza, and takes place mostly on the European continent.
It also has much less of an emphasis on 17th-century science than the first book, delving more into that era's political and economic developments. (Indeed, so much of the action of this book revolves around schemes relating to the buying and selling of shares of stock that I was both bored and somewhat confused for long stretches in the middle. Finance is like intellectual Kryptonite to me; can't understand it, have zero interest in understanding it.)
Anyway, the characters. Half-Cocked Jack sounds like someone took the most dramatic, colorful elements from Dickens (Jack's motherless childhood with his brother Bob, earning money hanging onto condemned men's legs as they swung from the gallows, ensuring a somewhat quicker death), Hunter S. Thompson (Jack is slowly losing his mind to syphilis, and as his side of the story progresses he becomes increasingly prone to vivid hallucinations which he cannot distinguish from reality), Jonathan Swift (in the frankly scatological descriptions of the kind of life Jack leads - hygiene is apparently a luxury a 17th-century Vagabond learns to do without), John Kennedy Toole and Gary Shteyngart (Jack's lewdness, sensuality and his knack for accidental heroism), and blended them all together in a single character. The actual experience of reading about this character's adventures is only slightly less awesome than whatever you've conjured up in your head while reading the previous sentence; the only problem is that they're so disjointed and episodic there's no sense of narrative momentum, just one damn thing after another.
The other main character is Eliza, a beautiful woman Jack rescues from a Turkish army camp during one of his brief spells of soldiering. When she first appeared, I wasn't sure I'd like her: her first interaction with Jack is a strained, eyeroll-inducing stretch of sexualized banter revolving around the tired, ages-old "battle of the sexes" scenario: the man has every kind of power imaginable over the woman, but because he desires her, that somehow evens the scales, or even secretly gives her the upper hand. Whatever. But luckily, Eliza is more than that: she's incredibly clever and a gifted storyteller, spinning tall tales that captivate Jack, who has lived more tall tales than most people have even heard. Like Scheherazade, she doles out portions of her life story (how she came to be a slave in a Turkish officer's tent, for instance, when she is a European woman who speaks English) strategically to make sure Jack keeps her with him long enough for her to get where she wants to go, which is Amsterdam.
Once Eliza gets to Amsterdam, she and Jack split up; she stays put, hoping to get in on the expanding mercantile economy and getting swept up in a scheme involving shares in a silver mine somewhere in the mountains of Germany, which gets her running in such high-rolling circles that she runs into a couple of lordly types who seize the opportunity to use her to further their various political intrigues. Her story gets more and more interesting and suspenseful as the stakes of her game rise and the rules get more complex; Jack's, on the other hand, seems to lose steam once he parts company with her. He continues to wander around Europe, with some vague notions of selling the fine warhorse and other loot he picked up in Turkey and thereby financing x more years of Vagabond life, and maybe also leaving something for his children. (He's never met them, but he knows he has some). He goes from place to place, stuff happens to him, he is increasingly unable to distinguish what's really happening from his hallucinations, which tend to resemble Elizabethan morality plays. It's all fairly anticlimactic, even though there are a couple of really awesome episodes. The book seems arbitrarily cut off at the end, for both of them, though. Eliza's arc in particular still seems to be building toward a future climax when the narrative ends and the (very long) section cataloguing the Dramatis Personae begins.