There are many discussions on the Ubuntu forums that compare Windows and Linux, and most non-newbies tend to tire quickly of the whole topic. Windows and Linux have major similarities and differences in functionality worth discussing when talking to someone who's wondering why they would ever bother with Linux. In fact, I recently checked out a book from the library that I had glanced at a couple of years ago called Moving from Windows to Linux, and that book's entire discussion centers on how things work in Linux and its "free as in beer" quality without discussing at all the implications of the GPL and open source code. But that's why I think the Windows vs. Linux functionality discussion should only be had after you've decided you're on board with free/open source software. And at that point, the whole question of "Does Linux work better than Windows?" is asked in the proper context.
Comparing the product Windows with the product Linux can bring mixed opinions, especially if all you know is Windows. Of course, even this feature by feature comparison is difficult, given the magnitude of variables on the Linux end of the scale. The very funny Mac vs. Windows ads with the frumpy, suited, older Windows guy and the laid back, bluejeans-clad Mac hipster show how cool trumps corporate every time, but what makes this comparison possible is the monolithic nature of each operating system. For a comparable Linux vs. Windows ad, you'd have the frumpy guy on the left and a huge group of people, each with her or his own personality, preferences, appearances, goals, and ideals on the right. Linux is not monolithic. It is a large and myriad community, so such comparisons are not truly possible.
The ultimate difference between Windows and Linux, though, is about goals. I just went to a training session at the library for one of the most prevalent library databases and it was led by a representative of that company. He's a sales rep and he talked like one - mentioning things like customer retention and besting the competition (Librarians vs. Google), and he did a lot of name dropping of high-profile corporate customers and his main thrust for us seemed to be that his company's product is just the best one out there. He was nice enough, and I don't mean to be condescending - he just misjudged his audience. His goals are to sell his product (which we've subscribed to for many years and have no plans to cancel - it is a high-quality reference database) and to inspire brand loyalty. Our goals as librarians are to know our resources for the end goal of high-quality information provision. You can say that this amounts to the same thing, but the difference in goals is key to any further discussion.
This point is the same with any Windows vs. Linux discussion. The goal of Microsoft is to make money. The goal of Linux distribution providers are usually to provide a free, high-quality operating system that can be shared without a license, etc.
Of course, the short answer to the question is "Linux is better." :-)