One of the questions I get asked a lot is the "KDE vs GNOME" question. My first reaction is "that's not the issue," – the message I want to send the world is not why GNOME is better than KDE. That would be constraining our message to people that already know and use open source desktops. I can tell you why GNOME is better than KDE in many circumstances and I'm sure KDE folks can tell you about circumstances where KDE is the better solution. And that's good.
GNOME's goal is to create a free and open source desktop. With that goal in mind, KDE is on the same team as GNOME – we are teammates working on free and open source computing solutions. We compete, but it's the friendly competition of teammates, each trying to win the valuable player award and pushing each other to our limits. The projects we compete together against are the non free desktops.
If GNOME has a competitor it's the non-free desktops of the world. I say "if we have a competitor" because I think we'll be stronger if we focus on being a free and open source desktop with a great user experience instead of focusing on our competition. We want to force them to hurry up and catch up with us by creating great projects that work for the user in ways our competitors haven't even dreamed of yet.
Update: I should have also pointed out that GNOME and KDE are working together. We've worked on projects like DBus together as well as planning to hold the GNOME and KDE conferences in the same location next summer so that developers can meet and collaborate.