Reading some of the other reviews might well give you the idea you won't learn much from this book. Unlike the Visual Studio based stuff, it doesn't cover how to use the IDE to create forms and projects. However, it does show you how to use the .NET framework from C#, just as "Programming Windows" showed you how to use the Windows API from C.
In my experience, knowledge of what's happening behind the scenes of a flashy IDE or wizard will help you make your code more reliable, more robust, and give you a better understanding of the development as a whole.
It's an ideal book to start with, especially if you take into account the fact you don't NEED to buy any software to make use of it. You can just download the 1.1 Framework and SDK, a copy of SharpDevelop, and you can start learning today!
I also have the Troelsen book, and it would be very hard to choose between them. The subjects in Petzold are all familiar, since I've been developing under Windows for some time, so it would really be a question of whose style you prefer. (I bought both).
All in all, an excellent first C#/.NET book to have.