The desktop problem has been solved many years ago. I mean, try to compare Windows XP with KDE 3:
nobody in their right mind would choose Windows over GNU/Linux based on the desktop experience alone.
The Web problem has also been solved. Microsoft clearly lost the Web war — they failed to enhance the Web in a proprietary way. What remains are some legal issues on the multimedia side that can be mostly worked around, the office documents formats issue and the flood of applications that only run on Windows, mostly games.
To me personally, two things matter the most.
First, how easy is it to develop applications that really utilise the power of the underlying platform? Keep in mind that those ‘desktops’ really are software development platforms, what you see on the screen is just the tip of the iceberg.
And second, is it free, in the liberty sense of the word? Do I get the source code? Can I learn from it? Can I modify it? Can I share my modifications with others?
Imagine where the world of computer science would be without Free Software! How much secret knowledge would be kept behind closed doors? Without us, people would study computer science and programming without ever having seen a real program in its entirety. That’s like becoming writers without ever having read a complete book.