Well, I've finished Stross' Hidden Family. I read it in one sitting, which is pretty unusual for me these days, and should tell you something about how good it was.
It's hard to review this book without mentioning Zelazny, so I won't try, except to say I'm confident you can thoroughly enjoy the Family Trade books without knowing anything about the Amber series. This series offers every bit as much devious family scheming, deceiving, and backstabbing as Zelazny's (and Betancourt's respectable effort at a prequel series) did, with novel twists. But there are vast differences as well: where Roger was poetic, Charles is practical. Zelazny wrote dreamingly of silver towers and a magical semi-deity Unicorn, Stross writes fervent praise of the effects of compounding productivity/economic enhancements and bringing democratic principles to a police state. It was wonderful to see the words of Adam Smith and Thomas Hobbes being discussed and applied -- and Karl Marx has a surprising part which I won't spoil. Stross takes the multiverse idea in a different and interesting direction, looking more seriously at the idea of alternate histories.
I could write more, but I've got get to sleep and I don't want to give too much away. All in all, one of the best books I've read in a while. But then, I seem to say that about all Stross' books. I feel obligated to say thanks again to Instapundit for introducing me to his work; I think that recommendation remains one of the best things I ever got from Glenn's blog.
Here's my earlier thoughts on the series, just before reading this book.