I've been using Windows for years, but recently spent several weeks living in Linux instead, as I write about in "Living free with Linux: 2 weeks without Windows." What I found was a solid, stable, operating system with a simple, easy-to-use interface, and that requires only lightweight hardware.
I've also been using Windows 7 since its pre-beta release, and most recently reviewed the Windows 7 beta in "Review: Windows 7 Beta 1 shows off new task bar, more UI goodies." Windows 7 is clearly faster than Vista, and includes plenty of nifty new interface features and productivity-boosting tools such as better search and document management.
So which is better suited for netbooks? For the mass consumer audience, there's little doubt: Windows 7 is superior. Installing new software and updating existing software in Linux isn't for the faint-hearted, and most people won't be able to figure out how to do it. In addition, Windows 7 has eye candy and extra features that Linux lacks. Most people also won't want to tackle the learning curve they'll face when moving from Windows to Linux.
Beyond that, Microsoft will spend countless millions of marketing dollars pushing Windows 7, and you can bet a good portion of that will go toward promoting it on netbooks. Since no one company owns Linux, there won't be any marketing muscle for Linux.
With all that being said, a Linux-based netbook should cost less than a Windows 7-based one. The operating system costs will be less, and depending on the version of Linux installed, may be zero. In addition, Linux can work with lighter-weight hardware than Windows 7, and so the hardware costs can be less as well.
So Linux won't completely vanish on netbooks, but Linux netbooks will become a small niche, primarily for budget-conscious technically oriented users. Estimates are that right now, about 30% of netbooks ship with Linux on them. Expect that number to plummet when Windows 7 ships.
Update: Microsoft says that sales of netbooks have taken a big bite out of its bottom line. For details see my blog post, "Microsoft layoffs: Netbook sales are killing us."